Chiral Anomaly

Many thanks to Norman Page, the fermion equation is the chiral Dirac equation, e.g. UFT248 ff. and the fermion equation has been intensively studied. There should be no problem in addressing the chiral anomaly with the fermion equation. Readers are encouraged to address this problem on their own initiative.

Papers

Myron The full texts are paywalled Norman

Chiral anomaly without relativity

  1. Anton Burkov

+ Author Affiliations

  1. Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, and National Research University ITMO, St. Petersburg 197101, Russia.
  1. E-mail: aburkov

Summary

The Dirac equation, which describes relativistic fermions (like electrons moving at nearly the speed of light), has a mathematically inevitable but puzzling feature: negative-energy solutions. The physical reality of these solutions is unquestionable, as one of their direct consequences—the existence of antimatter—is confirmed by experiment. However, the interpretation of the solutions has always been somewhat controversial. Dirac’s own idea was to view the vacuum as a state in which all the negative energy levels are physically filled. This “Dirac sea” idea seems to contradict a common-sense view of the vacuum as a state in which matter is absent. On the other hand, the Dirac sea is a very natural concept from the point of view of condensed matter physics, as there is a direct and simple analogy: filled valence bands of an insulating crystal. There exists, however, a phenomenon within the context of relativistic quantum field theory, whose satisfactory understanding seems to be hard to achieve without assigning physical reality to the Dirac sea. This phenomenon, the chiral anomaly, presents a quantum mechanical violation of chiral symmetry; it was first observed experimentally in particle physics as a decay of a neutral pion into two photons. On page 413 of this issue, Xiong et al. (1) report the observation of this phenomenon in a condensed matter system—a crystal of Na3Bi—manifesting as an unusual negative longitudinal magnetoresistance; the vacuum/insulating crystal analogy is now all the more tangible.

Read the Full Text

Evidence for the chiral anomaly in the Dirac semimetal Na3Bi

  1. Jun Xiong1,
  2. Satya K. Kushwaha2,
  3. Tian Liang1,
  4. Jason W. Krizan2,
  5. Max Hirschberger1,
  6. Wudi Wang1,
  7. R. J. Cava2,
  8. N. P. Ong1,*

+ Author Affiliations

  1. 1Department of Physics, Princeton University, Princeton, NJ 08544, USA.
  2. 2Department of Chemistry, Princeton University, Princeton, NJ 08544, USA.
  1. npo

In a Dirac semimetal, each Dirac node is resolved into two Weyl nodes with opposite “handedness” or chirality. The two chiral populations do not mix. However, in parallel electric and magnetic fields (E||B), charge is predicted to flow between the Weyl nodes, leading to negative magnetoresistance. This “axial” current is the chiral (Adler-Bell-Jackiw) anomaly investigated in quantum field theory. We report the observation of a large, negative longitudinal magnetoresistance in the Dirac semimetal Na3Bi. The negative magnetoresistance is acutely sensitive to deviations of the direction of B from E and is incompatible with conventional transport. By rotating E (as well as B), we show that it is consistent with the prediction of the chiral anomaly.

Computer Algebra

Agreed, since Horst joined AIAS in about 2007 computer algebra and checking has always been applied whenever possible. In any new institute computer algebra would be part of the scene. It is routine now in every laboratory. I implemented an early form this method in Room 262 on the Elliott 4130 as in Autobiography Volume Two. The advances in computation since then are already legendary.

To: EMyrone@aol.com
Sent: 29/10/2015 08:32:30 GMT Standard Time
Subj: Re: FOR POSTING : Final Version of UFT330 Sections 1 and 2

Said this many times before but these computer checks are fantastic and so important. Einstein would probably have seen some of the flaws he introduced himself had this tool been available in his life time.

Sent from my Samsung device

Discussion of Extra Structure of the Relativistic Zeeman Effect

Many thanks, I plan to send the finished note off today, using notes for UFT306 on the Evans / Morris effects. I envisage a new spectroscopy laboratory at any AIAS Institute that may develop at Aberystwyth where instruments and computers (possibly a supercomputer) would be assembled to test these predictions experimentally. Other parts of the Institute would develop a whole pile of discoveries made since 1971 (OO and UFT sections of www.aias.us). The advantage of affiliation with UCW Aberystwyth is eligibility to apply for grants. The model is the historic Room 262 at the EDCL. There is also a need to implement the Delta Project of the European Molecular Liquids Group (Omnia Opera 99) using the tremendous advances made since I wrote the plans for Delta as the EMLG’s first scientific coordinator. There would also be energy from spacetime and LENR laboratories. I dsicussed plans for an EMLG laboratory at Aberystwyth with the late Rt. Hon Tam Dalyell, then shadow minister for education. All these plans had to be shelved for non scientific reasons as in Autobiography volume two but they could be implemented anywhere in the world at any time. If this institute joined forces with the group of Sir John Meurig Thomas and Prof. Sir Martin Evans (a Nobel Laureate in biochemistry and genetics in Cardiff), it would be a powerful institute. There would be a Nobel Laureate and two Nobel nominees.

To: EMyrone@aol.com
Sent: 28/10/2015 17:05:35 GMT Standard Time
Subj: Re: Extra Structure of the Relativistic Zeeman Effect

Congratulations yet again. Very important!!

Sent from my Samsung device

Discussion of Note 330(7)

These results are the first time that the Dirac equation has been developed without using his rough approximation, and they can be compared directly with spectral data. They are worked out in the first approximation with the non relativistic H wavefunctions, which for H is a good approximation. I will correct the errata shortly. Section 3 has already been posted as mentioned by Horst and contains a comparison of expectation values of 1 / r cubed and 1 / r fourth and a computation of the new terms. At present I am working on UFT331 and a new type of relativistic Zeeman spectroscopy. All these results are being recorded and could be tested experimentally at an AIAS institute at Aberystwyth, and also of course elsewhere. This method can also be developed extensively with computational quantum chemistry code libraries around the world, for example IBM MOTECC for which I was the lead writer at IBM Kingston, New York State, in 1988. Well developed code for the Dirac equation can be modified, producing many new spectral patterns of immediate use to analytical and pathological laboratories for example, using Fourier transform IR, ESR and NMR, and also MRI.

To: EMyrone@aol.com
Sent: 28/10/2015 13:50:41 GMT Standard Time
Subj: PS: Re: Discussion of Note 330(7)

Attachment was missing 🙂

Am 28.10.2015 um 14:49 schrieb Horst Eckardt:

I computed <U> and <Hso2> by Maxima, see last two formulas in the protocol. In <U> (eq.29) some factors are wrong, probably the Bohr radius (%o8) was not correctly inserted. in (30) a factor c^2 is superflous and m squared reduces to m.

I had already sent over section 3 of the paper.

Horst

Am 28.10.2015 um 09:58 schrieb EMyrone:

Many thanks for going through this. The dimensionality of Eq. (30) appears to be correct. The term in brackets is energy and when divided by m c squared is dimensionless. So the term becomes the usual gyromagnetic ratio (e h bar / (2m)) multiplied by sigma dot B multiplied by a dimensionless constant. This can be run through Maxima to double check. Very many new ESR, NMR, MRI and Zeeman and anomalous Z|eeman spectroscopies emerge – again by scholarly scrutiny of the ninety year old basics. I think that there will also be a whole pile of new results in nonlinear optics and quantum optics. Something for the younger generations to think about. In ECE two all this theory is related to torsion and curvature and spin connection.

To: Emyrone
Sent: 27/10/2015 19:45:50 GMT Standard Time
Subj: note 330(7)

How did you get the constants in eq.(30)? Eq. (28) is

< 1/r > = 1 / (n^2*a0)

with Bohr radius a0. Inserting this into (27) gives (30) but with m
instead of m squared. I do not know if (29) is correct.

Horst

330(7).pdf

Discussion of Note 330(7)

OK thanks, I will correct these errata and send the final version of UFT330 for reposting.

To: EMyrone@aol.com
Sent: 28/10/2015 13:49:54 GMT Standard Time
Subj: Re: Discussion of Note 330(7)

I computed <U> and <Hso2> by Maxima, see last two formulas in the protocol. In <U> (eq.29) some factors are wrong, probably the Bohr radius (%o8) was not correctly inserted. in (30) a factor c^2 is superflous and m squared reduces to m.

I had already sent over section 3 of the paper.

Horst

Am 28.10.2015 um 09:58 schrieb EMyrone:

Many thanks for going through this. The dimensionality of Eq. (30) appears to be correct. The term in brackets is energy and when divided by m c squared is dimensionless. So the term becomes the usual gyromagnetic ratio (e h bar / (2m)) multiplied by sigma dot B multiplied by a dimensionless constant. This can be run through Maxima to double check. Very many new ESR, NMR, MRI and Zeeman and anomalous Z|eeman spectroscopies emerge – again by scholarly scrutiny of the ninety year old basics. I think that there will also be a whole pile of new results in nonlinear optics and quantum optics. Something for the younger generations to think about. In ECE two all this theory is related to torsion and curvature and spin connection.

To: Emyrone
Sent: 27/10/2015 19:45:50 GMT Standard Time
Subj: note 330(7)

How did you get the constants in eq.(30)? Eq. (28) is

< 1/r > = 1 / (n^2*a0)

with Bohr radius a0. Inserting this into (27) gives (30) but with m
instead of m squared. I do not know if (29) is correct.

Horst

Daily Report 27/10/15

There were 2175 hits or files downloaded from 373 distinct visits or reading sessions up to half hour default, main spiders baidu, google, MSN, yandex and yahoo. Top ten UFT papers 918, Collected ECE2 558, Collected Evans / Morris 540(est), Collected scientometrics 514, F3(Sp) 491, Barddoniaeth / Collected poetry 282, Autobiography volumes one and two 264, Proofs that no torsion means no gravitation 164, Eckardt / Lindstrom papers 161, Principles of ECE 141, Engineering Model 138, UFT88 116, Evans Equations 87 (numerous Spanish), CEFE 69, UFT311 43, Llais 41, UFT321 36, UFT313 29, UFT314 26, UFT315 26, UFT316 22, UFT317 33, UFT318 42, UFT319 34, UFT320 29, UFT322 35, UFT323 23, UFT324 49, UFT325 41, UFT326 44, UFT327 33, UFT328 43, UFT329 43, UFT330 6 to date in October 2015. Cornell University UFT177 on the quantum force equation; New York University Tandon School of Engineering general; Princeton University UFT214; Texas A and M University UFT25, UFT104; Berri Medical Library Spain my page; Seville University general; Leiden University UFT213; Edu system Pakistan UFT25; Joint Institutes for Nuclear Research Dubna Russian Federation UFT41; University College London educational note two. Intense interest all sectors, updated usage file attached for October 2015

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Discussion of Note 330(7)

Many thanks for going through this. The dimensionality of Eq. (30) appears to be correct. The term in brackets is energy and when divided by m c squared is dimensionless. So the term becomes the usual gyromagnetic ratio (e h bar / (2m)) multiplied by sigma dot B multiplied by a dimensionless constant. This can be run through Maxima to double check. Very many new ESR, NMR, MRI and Zeeman and anomalous Z|eeman spectroscopies emerge – again by scholarly scrutiny of the ninety year old basics. I think that there will also be a whole pile of new results in nonlinear optics and quantum optics. Something for the younger generations to think about. In ECE two all this theory is related to torsion and curvature and spin connection.

To: Emyrone@aol.com
Sent: 27/10/2015 19:45:50 GMT Standard Time
Subj: note 330(7)

How did you get the constants in eq.(30)? Eq. (28) is

< 1/r > = 1 / (n^2*a0)

with Bohr radius a0. Inserting this into (27) gives (30) but with m
instead of m squared. I do not know if (29) is correct.

Horst

FOR POSTING: Section 3 of UFT327

This is a very important section 3 by co author Horst Eckardt because it refutes the claim that Einsteinian general relativity produces planetary precession, a brilliant ray of light after a hundred years of dogma of the darkened cave. This major discovery again shows the importance of subjecting a load of old dogma (or cobblers) to scholarly scrutiny using the power of computer algebra. This gets rid of the often hair raising and obscure approximations used by Einstein. All these errors cast grave doubt on all his work in general relativity, although the idea of basing physics on geometry is still intact. This idea goes back to ancient civilizations. It has become obvious that the Einstein theory worked out in this way does not produce precession AT ALL. The UFT papers show in many other ways that the theory is totally wrong. The most ridiculous results came out of the Marion and Thornton approximation. The dogmatists have not been able to formulate a single logical reply. Abuse and trolling does not of course count as science. It is in fact a criminal activity. The dogmatists became so arrogant that they started to abuse real scholars. We all can feel that we are witnessing history in the making, and major surgery was needed for the truth to come out. It turns out that it is special relativity that gives the true precessing orbit (UFT324 and UFT325 and essays). This is worked out by computer algebra using simultaneous solution of the lagrangian and hamiltonian of special relativity, with no other assumption. Stephen Crothers was always right, and if he is interested, should be appointed a full professor with tenure at one of the top twenty universities in the world, so of course should Horst Eckardt and others of AIAS if they are interested. The educational system of AIAS is already as good as anything in the world. A reinvigorated chemistry department at Aberystwyth would be an ideal place for an AIAS Institute for those willing to learn Welsh. I think that the University of Muenich could consider a post for Horst Eckardt and British Columbia a post for Douglas Lindstrom. These are two world ranking universities.

Sent: 27/10/2015 16:00:30 GMT Standard Time
Subj: Section 3 of paper 327

This is the discussion of the Einstein solution of orbital precession,
but there is none.

Horst

paper327-3.pdf