TY - GEN

T1 - Nöther’s Second Theorem as an Obstruction to Charge Quantization

AU - Phillips, Philip

AU - La Nave, Gabriele

N1 - Funding Information:
We thank K. Limtragool for a collaboration on the Aharonov-Bohm effect and E. Witten and S. Avery for insightful remarks and DMR19-19143 for partial support.
Publisher Copyright:
© 2020, Springer Nature Singapore Pte Ltd.

PY - 2020

Y1 - 2020

N2 - While it is a standard result in field theory that the scaling dimension of conserved currents and their associated gauge fields are determined strictly by dimensional analysis and hence cannot change under any amount of renormalization, it is also the case that the standard conservation laws for currents, remain unchanged in form if any differential operator that commutes with the total exterior derivative, multiplies the current. Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of Nöther’s second theorem. We review here our recent work on one particular instance of this theorem, namely fractional electromagnetism and highlight the holographic dilaton models that exhibit such behavior and the physical consequences this theory has for charge quantization. Namely, the standard electromagnetic gauge and the fractional counterpart cannot both yield integer values of Planck’s constant when they are integrated around a closed loop, thereby leading to a breakdown of charge quantization.

AB - While it is a standard result in field theory that the scaling dimension of conserved currents and their associated gauge fields are determined strictly by dimensional analysis and hence cannot change under any amount of renormalization, it is also the case that the standard conservation laws for currents, remain unchanged in form if any differential operator that commutes with the total exterior derivative, multiplies the current. Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of Nöther’s second theorem. We review here our recent work on one particular instance of this theorem, namely fractional electromagnetism and highlight the holographic dilaton models that exhibit such behavior and the physical consequences this theory has for charge quantization. Namely, the standard electromagnetic gauge and the fractional counterpart cannot both yield integer values of Planck’s constant when they are integrated around a closed loop, thereby leading to a breakdown of charge quantization.

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U2 - 10.1007/978-981-15-7775-8_9

DO - 10.1007/978-981-15-7775-8_9

M3 - Conference contribution

AN - SCOPUS:85094097238

SN - 9789811577741

T3 - Springer Proceedings in Mathematics and Statistics

SP - 135

EP - 150

BT - Lie Theory and Its Applications in Physics, 2019

A2 - Dobrev, Vladimir

PB - Springer

T2 - 13th International Workshop on Lie Theory and Its Applications in Physics, LT 2019

Y2 - 17 June 2019 through 23 June 2019

ER -