Theoretical Physics | Quantum Biology | Dark Matter Research Cluster

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Open thread: Self-accelerating Dirac particles and prolonging the lifetime of relativistic fermions

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3196.html

A gauge field (field), let's say by its quantum phase, is able to cause quantum effects!

Forces and effects in nature are linked to symmetries in the universe (e.g. have a look at Euler-Lagrange) and the laws of energy conservation (e.g. Noethers theorem).

In the post above, scientists are linking the quantum world to the real world by observing the wave(function) of an electron in a region of space with zero electromagnetic field.

This is what Dirac's equations tried to solve: when describing energy mathematically by linking real or relativistic world (Einstein) with quantum world (FTL (positrons) , Pauli, energy) the (2nd derivative of) Klein Gordon Equation induced a negative probability density which could not be explained. Aren't electrons supposed to seek for an overall equilibrium in space, just changing to a lower energy state? Shouldn't there be a Dirac Sea?http://en.wikipedia.org/wiki/Dirac_sea

The "holes" that Dirac predicted were revealed as positrons, the opposing charge of electrons and charge of antimatter.

We are talking by defining quantum states of energy of quantum spin, charge and different quantum states.

http://en.wikipedia.org/wiki/Dirac_equation

Now, the post is about the Aharonov–Bohm effect:

"The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic field (E, B), despite being confined to a region in which both the magnetic field B and electric field E are zero. The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wavefunction, and the Aharonov–Bohm effect is accordingly illustrated by interference experiments.

The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle's wavefunction being negligible inside the solenoid. This phase shift has been observed experimentally.[1] There are also magnetic Aharonov–Bohm effects on bound energies and scattering cross sections, but these cases have not been experimentally tested. An electric Aharonov–Bohm phenomenon was also predicted, in which a charged particle is affected by regions with different electrical potentials but zero electric field, but this has no experimental confirmation yet.[1] A separate "molecular" Aharonov–Bohm effect was proposed for nuclear motion in multiply connected regions, but this has been argued to be a different kind of geometric phase as it is "neither nonlocal nor topological", depending only on local quantities along the nuclear path.[2]

Werner Ehrenberg and Raymond E. Siday first predicted the effect in 1949,[3] and similar effects were later published by Yakir Aharonov and David Bohm in 1959.[4] After publication of the 1959 paper, Bohm was informed of Ehrenberg and Siday's work, which was acknowledged and credited in Bohm and Aharonov's subsequent 1961 paper.[5][6] Subsequently, the effect was confirmed experimentally by several authors; a general review can be found in Peshkin and Tonomura (1989)."

http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect

And it says:

"The Aharonov–Bohm effect predicts that two parts of the electron wavefunction can accumulate a phase difference even when they are confined to a region in space with zero electromagnetic field. Here we show that engineering the wavefunction of electrons, as accelerating shape-invariant solutions of the potential-free Dirac equation, fundamentally acts as a force and the electrons accumulate an Aharonov–Bohm-type phase—which is equivalent to a change in the proper time and is related to the twin-paradox gedanken experiment. This implies that fundamental relativistic effects such as length contraction and time dilation can be engineered by properly tailoring the initial conditions. As an example, we suggest the possibility of extending the lifetime of decaying particles, such as an unstable hydrogen isotope, or altering other decay processes. We find these shape-preserving Dirac wavefunctions to be part of a family of accelerating quantum particles, which includes massive/massless fermions/bosons of any spin."

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3196.html

Now, please be aware of Pauli's exclusion principle: this is a fundamental principle in order to understand how energy/charge and by that quantum spin (fermions/bosons) is partitioned by space (A Black Hole Lens, enabling antimatter to be stable at this side of an apparant horizon, antimatter is shielded by an EM-field) http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html

The wavefunction of an electron:

We can look upon the wave function of the electron as a confined helical wave with a forward component (zig) and a reverse component (zag), that explains the zig-zag of the electron.

Neutrinos without any mass would be a left-handed spinor, comparable to the forward zig -wave of an electron. In case they have a tiny mass and are able to oscillate, it is possible that they interact with the vacuum field as part of a reverse zag wave.

http://copaseticflow.blogspot.de/2013/05/solar-neutrinos-and-radioactive-decay.html

Well, please just try to comprehend some hints I have given you. I know that my explantions are still missing the "last act in order to let people fly" on this, but you should be able to solve this puzzle for yourself, time after time..

Science is not made by gathering just knowledge, but a result of curiosity and passion.

I will provide some more useful links:

http://www.nature.com/nature/journal/v463/n7277/full/nature08688.html

http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout_2_2011.pdf

http://www.physics.ucdavis.edu/~cheng/teaching/230A-s07/rqm3_rev.pdf

"

I would like to quote +Randy Curry (Google Plus) here, who wrote this fabulous comment on this shared post in his stream:

"This would reduce the cost of particle colliders like the LHC, and make funding research into the basic structure of the cosmos much easier. This has the potential to progress our understanding, and therefore technology, faster than ever thought possible. Testing theories such as M-Theory would cost a fraction of what it took to accelerate the first particle. The possibilities are all but endless." Thanks a lot for this, Randy!

Quote: "Similarly, the Aharonov–Bohm effect illustrates that the Lagrangian approach to dynamics, based on energies, is not just a computational aid to the Newtonian approach, based on forces. Thus the Aharonov–Bohm effect validates the view that forces are an incomplete way to formulate physics, and potential energies must be used instead. In fact Richard Feynman complained[citation needed] that he had been taught electromagnetism from the perspective of electromagnetic fields, and he wished later in life he had been taught to think in terms of the electromagnetic potential instead, as this would be more fundamental. In Feynman's path-integral view of dynamics, the potential field directly changes the phase of an electron wave function, and it is these changes in phase that lead to measurable quantities."

http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect#Global_action_vs._local_forces

I was thinking of this quantum effect of Aharonov-Bohm could be related to the exchange of phonons and superpositional states by electrons in space vacuum. There is also a close relation of solenoidal (maths) and source free (physics, maxwell), because the fields in vacuum are changing their density (energy is like a perfect fluid, hence the relativistic quantum vacuum is behaving like a bubble of air below water in aphelion and perihelion phases, changigs its density, the fine structure constant alpha is chaning, even radiation decay rates are chaning with sun activity (neutrinos are oscillating)):

We might encounter here an effect by phase transition of real world to quantum world (FTL!) : the photon is an information boson ...

Any yes, on Wikipedia there is this thought of a source free space vacuum...

Monopoles and Dirac strings

The magnetic Aharonov–Bohm effect is also closely related to Dirac's argument that the existence of a magnetic monopole can be accommodated by the existing magnetic source-free Maxwell's equations if both electric and magnetic charges are quantized.

A magnetic monopole implies a mathematical singularity in the vector potential, which can be expressed as a Dirac string of infinitesimal diameter that contains the equivalent of all of the 4πg flux from a monopole "charge" g. The Dirac string starts from, and terminates on, a magnetic monopole. Thus, assuming the absence of an infinite-range scattering effect by this arbitrary choice of singularity, the requirement of single-valued wave functions (as above) necessitates charge-quantization. That is, 2\frac{q_\text{e}q_\text{m}}{\hbar c} must be an integer (in cgs units) for any electric charge qe and magnetic charge qm.

Like the electromagnetic potential A the Dirac string is not gauge invariant (it moves around with fixed endpoints under a gauge transformation) and so is also not directly measurable.

http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect#Monopoles_and_Dirac_strings

http://en.wikipedia.org/wiki/Gauge_fixing

And this one, me thinks that there is a correlation to this post:

*Fibre Bundle, Gauge Theory, Instanton Moduli Space and

Instanton Tunneling Effect*

The connection between gauge theory and the geometry of fibre bundle is very dramatic. The

non-Abelian gauge theory was proposed by theoretical physicists Chen-Ning Yang and Robert

Mills in the early middle of 1950s [1]. At that time, the fibre bundle theory had already developed

ripely in differential geometry, but physicists almost know nothing about it. It is until

early 1960s that a theoretical physicist Elihu Lubkin realized that the classical Yang-Mills gauge

theory and the affine geometry of fibre bundle are identical [2]. A gauge field is actually the

pull-back of the connection to the base manifold of a certain principle fibre bundle and the gauge

field strength is the pull-back of the curvature of principle bundle, while the gauge group is the

structure group of principle bundle. Further, matter fields can be considered as the sections of

some associated bundles of the principle fibre bundle, and the gauge transformation is the action

of structure group on the section of associated bundle. However, these facts had not been taken

3seriously by physicists. The extensive application of fibre bundle geometry in gauge theory was

caused by an article on the global structure of electromagnetic field written by Tai-Tsun Wu

and Chen-Ning Yang in 1975 [3]. In this article, they defined the electromagnetic potential on

two half spheres S

2 with overlapping and avoided the singular string problem in the magnetic

potential produced by the Dirac monopole [4]. In the overlapping region of two spheres, the

magnetic potentials are related by a U(1) gauge transformation. The geometry of this physical

system is precisely a principle U(1)-bundle with base manifold S

2

[3]. In the the same year Wu

and Yang published their paper, A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Yu.S. Tyupkin

from the former Soviet Union found a solution to the classical SU(2) Yang-Mills theory with

finite action in the Euclidean space [5], which is now called the BPST instanton (due to the

physical effect it produces which will be mentioned later). This solution describes a gauge field

configuration with (anti-)self-dual field strength, and its geometrical description is the principle

SU(2)-bundle on the base manifold S

4

. Further, it had been realized that this solution has

topological meaning, and it is characterized by a topological index, which is precisely the Chern

number of the second Chern Class in fibre bundle theory [6]. The BPST instanton is actually

a classical solution to the Euclidean SU(2) Yang-Mills theory with the Chern number equal to

one. In the following years, theoretical physicists including Edward Witten [7], E. Corrigan and

D.B. Fairlie [8], Roman Jackiw, C. Nohl and Claudio Rebbi [9] found multiple (anti-)instanton

solution with Chern number |k| > 1. Especially, Jackiw and Rebbi showed that the classical

Yang-Mills theory has not only non-Abelian gauge symmetry and the Poincar´e space-time symmetry,

but also a larger conformal space-time symmetry [10], which consists of the Poincar´e

symmetry composed of translational and Lorentz rotational invariance, dilatational invariance

and special conformal symmetry. As we know, if a field theory has a certain symmetry, then the

symmetry transformation on a space-time dependent classical solution should lead to another

solution to the equation of motion. This means that there exists a family of solutions to a field

theory with symmetries. The inequivalent solutions under symmetry transformations constitute

a finite-dimensional space, which is called the moduli space of classical solution. Concretely

speaking, if a space-time dependent solution to the classical equation of motion cannot manifest

a certain symmetry of the field theory explicitly, then there must have some parameter in the

solutions to characterize the symmetry. The number of independent parameters in the solution

is the dimension of the moduli space of the classical solution. At the late stage of 1970s, both

theoretical physicists and mathematicians employed various distinct methods to determine the

dimension of instanton moduli space. A.S. Schwartz [11] and Michael Atiyah, Nigel Hitchin and

Isadore Singer [12] used the celebrated Atiyah-Singer index theorem in algebraic geometry to

have identified the dimension of SU(2) instanton moduli space as 8|k| − 3. At the same time,

Jackiw and Rebbi [13], Lowell Brown, Robert Carlitz and Choon-Kyu Lee [14] determined the

dimension by analyzing degrees of freedom in the instanton solution and calculating the number

of fermionic zero-modes of the Dirac operator in the instanton background, respectively.

Moreover, the number of independent parameters for the instanton solution to the Yang-Mills

theory with a general gauge group was worked out by theoretical physicists Claude Bernard,

Norman Christ, Alan Guth and Erick Weinberg [15] as well as mathematician Atiyah, Hitchin

and Singer [16]. Further, mathematicians [17] solved the problem how to construct an instanton

solution for an arbitrarily given Chern number by using Roger Penrose’s twistor description [18]

to Yang-Mills theory. This construction showed the power of algebraic geometry in gauge theory

[17]. Finally, mathematicians proved that the finite action solution to a Yang-Mills theory on a

compactified Euclidean space in four dimensions must be an instanton solution [19]. At the end

4of 1970s, all the puzzles on instanton solution and the instanton moduli space had been cleared.

To summarize, the joint efforts made by both physicists and mathematicians at the late of 1970s

had laid the foundation for the breakthrough made in 1980s in understanding differential topological

structure of a simply-connected smooth four-manifold.

On the other hand, in the same time theoretical physicists started investigating physical

effects induced by instanton. In the middle of 1970s, Jackiw and Rebbi [20], Curtis Callan,

Roger Dashen and David Gross [21] found the vacuum structure of a non-Abelian gauge theory

is highly nontrivial: the Yang-Mills theory with gauge group SU(2) has vacua with an infi-

nite number of degeneracies. These vacua are classified into distinct homotopy classes by the

mapping from S

3

to SU(2) and characterized by topological indices. People usually thought

these topological vacua should be absolutely stable since topological numbers should prevent

the vacuum from decaying. However, the existence of instanton breaks this naive physical pattern.

Gerard ’t Hooft first studied quantum gauge theory in the instanton background [22].

He found that an instanton can cause the transition between two topological vacua if the difference

of their topological indices equals to the Chern number of the instanton. This is the

famous tunneling effects produced by instanton in a quantum gauge theory. A clear physical

interpretation on the tunneling effect in quantum chromodynamics was further given by Callan,

Dashen and Gross [23]. The tunneling phenomenon has lifted the degeneracy of topological

vacua and the true vacuum state is the so-called θ-vacuum, the superposition of the topological

vacua. However, if the theory has massless fermions, then the tunneling effect produced by

instanton disappears. The reason for this phenomenon is that a massless fermion carries not

only usual fermionic charge (electric charge, lepton number or baryon number, depending on

physical objects fermionic fields represent), but also a fermionic charge which changes sign under

mirror (parity) transformation. In physics, it is called that the massless fermionic theory has

a chiral symmetry (or equivalently axial vector UA(1) symmetry). However, in the presence of

instanton configuration, this symmetry is violated by quantum correction. Thus the fermionic

charge that flips a sign under mirror reflection transformation is not conserved and acquires a

contribution proportional to the instanton number, which is induced by quantum correction.

This phenomenon in physics is called that UA(1) symmetry suffers from chiral anomaly [24].

At the late stage of 1970s, it was realized that chiral anomaly is independent of perturbative

calculation of quantum field theory and has a topological origin. The violation of the axial

fermionic charge is equal to the difference of the left- and right-handed fermionic zero modes of

the Dirac operator in the instanton background [25]. This means that the Dirac operator acting

on the massless fermionic fields in the instanton background must have non-paired zero modes.

Since a fermionic field is represented by a Grassmann quantity, so the existence of non-paired

zero modes leads to vanishing integration over fermionic fields and hence the tunneling effect

is suppressed by massless fermions. ’ t Hooft used the integration property of the Grassmann

quantity to have realized that this phenomenon is actually a topological section rule for the

physical process. Some gauge invariant quantities carrying the fermonic charges which change

sign under parity transformation can absorb the fermionic zero modes and present non-vanishing

expectation values, and hence contribute to the ’t Hooft quantum effective action. ’t Hooft used

this idea to have solved the notorious UA(1) problem in particle physics.

The instanton background can also cause zero modes for the operators acting on bosonic

fields such as scalar and vector fields. However, the origins of these bosonic zero modes are

5completely different from the fermionic ones for the Dirac operator. As mentioned before, the

instanton solution must contain some parameters to manifest gauge and space-time symmetries

of the theory. The variations of these parameters do not alter the action or potential energy of

the theory. Therefore, the bosonic operators have zero modes along the directions represented

by these parameters. In physics one can consider these bosonic modes as the Goldstone modes

corresponding to the breaking of certain global symmetries in the directions represented by the

parameters. Viewed from the geometry of instanton moduli space, these bosonic zero modes

are actually tangent vectors to the moduli space and hence the number of these zero modes

is the dimension of the instanton moduli space, since the dimension of a tangent space to

a manifold is equal to the dimension of the manifold. One usually makes use of a so-called

collective coordinate method to handle the bosonic zero modes in quantum field theory. In the

path integral description of quantum field theory, the essence of collective coordinate method

is separating the integrations over zero modes from those non-zero modes. After the non-zero

modes have been integrated out, the path integration over the bosonic fields reduces to an

integration on the instanton moduli space and the key point in this process is how to define

the integration measure on the instanton moduli space. Note that this is actually the physical

idea used by Witten to describe the Donaldson invariant with a quantum gauge theory. It

should emphasize that the above mentioned ’t Hooft’s instanton calculus is a pioneer work in

non-perturbative calculation. During these past thirty years, most of important developments

in non-perturbative quantum field theory such as instanton calculus in supersymmetric gauge

theory [26, 27, 28, 29], topological quantum field theory [30] and the Seiberg-Witten duality [31]

are somehow the prolongs of ’t Hooft’s instanton calculus. ’t Hooft converted the complicated

calculation in the instanton background into a central potential problem in quantum mechanics,

and it is still not an easy task to repeat his calculations for a beginner despite that more than

thirty years have passed.

4 Supersymmetry, Supersymmetric Gauge Theory, R-symmetry

....