Noether’s theorems and conserved currents in gauge theories in the presence of fixed fields - INSPIRE

DataBETA

Noether’s theorems and conserved currents in gauge theories in the presence of fixed fields

Gabor Zsolt Toth
(
- Wigner RCP, Budapest
)

Oct 11, 2016

17 pages

Published in:

Phys.Rev.D 96 (2017) 2, 025018

Published: Jul 24, 2017

e-Print:

1610.03281 [gr-qc]

DOI:

10.1103/PhysRevD.96.025018

View in:

reference search4 citations

Citations per year

Abstract: (APS)

We extend the standard construction of conserved currents for matter fields in general relativity to general gauge theories. In the original construction, the conserved current associated with a spacetime symmetry generated by a Killing field hμ is given by -gTμνhν, where Tμν is the energy-momentum tensor of the matter. We show that if in a Lagrangian field theory that has gauge symmetry in the general Noetherian sense some of the elementary fields are fixed and are invariant under a particular infinitesimal gauge transformation, then there is a current Bμ that is analogous to -gTμνhν and is conserved if the nonfixed fields satisfy their Euler-Lagrange equations. The conservation of Bμ can be seen as a consequence of an identity that is a generalization of ∇μTμν=0 and is a consequence of the gauge symmetry of the Lagrangian. This identity holds in any configuration of the fixed fields if the nonfixed fields satisfy their Euler-Lagrange equations. We also show that Bμ differs from the relevant canonical Noether current by the sum of an identically conserved current and a term that vanishes if the nonfixed fields are on shell. For an example, we discuss the case of general, possibly fermionic, matter fields propagating in fixed gravitational and Yang-Mills background. We find that in this case the generalization of ∇μTμν=0 is the Lorentz law ∇μTμν-FaνλJaλ=0, which holds as a consequence of the diffeomorphism, local Lorentz and Yang-Mills gauge symmetry of the matter Lagrangian. For a second simple example, we consider the case of general fields propagating in a background that consists of a gravitational and a real scalar field.

Note:

28 pages, LaTeX, minor changes, journal reference added

symmetry: gauge
current: conservation law
matter: symmetry
symmetry: Noether
current: Noether
background: Yang-Mills
transformation: gauge
symmetry: space-time
diffeomorphism: invariance
tensor: energy-momentum

References(57)

Figures(0)

[1]

General Relativity

R.M. Wald

[2]

Some properties of Noether charge and a proposal for dynamical black hole entropy

Vivek Iyer
(
- Chicago U., EFI and
- Chicago U.
)
,
Robert M. Wald
(
- Chicago U., EFI and
- Chicago U.
)

- Phys.Rev.D 50 (1994) 846-864
•
e-Print:
- gr-qc/9403028
•
DOI:
- 10.1103/PhysRevD.50.846

[3]

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

László B. Szabados
(
- Budapest, RMKI
)

- Living Rev.Rel. 12 (2009) 4
•
DOI:
- 10.12942/lrr-2009-4

[4]

E. Noether

- Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen Mathematisch-Physikalische Klasse (1918) 1918

[5]

The Noether Theorems: Invariance and Conservations Laws in the Twentieth Century

Y. Kosmann-Schwarzbach

[6]

Test fields cannot destroy extremal black holes

- Class.Quant.Grav. 33 (2016) 17, 175002
•
e-Print:
- 1601.06809
•
DOI:
- 10.1088/0264-9381/33/17/175002

[7]

Comments on the Casimir energy in supersymmetric field theories

- JHEP 07 (2015) 001
•
e-Print:
- 1412.7463
•
DOI:
- 10.1007/JHEP07(2015)001

[8]

The Casimir Energy in Curved Space and its Supersymmetric Counterpart

Benjamin Assel
(
- King's Coll. London, Dept. Math
)
,
Davide Cassani
(
- Paris U., IV and
- Paris, LPTHE
)
,
Lorenzo Di Pietro
(
- Weizmann Inst.
)
,
Zohar Komargodski
(
- Weizmann Inst.
)
,
Jakob Lorenzen
(
- King's Coll. London, Dept. Math
)

et al.

- JHEP 07 (2015) 043
•
e-Print:
- 1503.05537
•
DOI:
- 10.1007/JHEP07(2015)043

[9]

Belinfante tensors induced by matter gravity couplings

Vadim Borokhov
(
- Caltech
)

- Phys.Rev.D 65 (2002) 125022
•
e-Print:
- hep-th/0201043
•
DOI:
- 10.1103/PhysRevD.65.125022

[11]

Wong's Equations and Charged Relativistic Particles in Non-Commutative Space

Herbert Balasin
(
- Vienna, Tech. U.
)
,
Daniel N. Blaschke
(
- Los Alamos
)
,
Francois Gieres
(
- Lyon, IPN
)
,
Manfred Schweda
(
- Vienna, Tech. U.
)

- SIGMA 10 (2014) 099
•
e-Print:
- 1403.0255
•
DOI:
- 10.3842/SIGMA.2014.099

[12]

Test of the weak cosmic censorship conjecture with a charged scalar field and dyonic Kerr-Newman black holes

Gabor Zsolt Toth
(
- Budapest, RMKI
)

- Gen.Rel.Grav. 44 (2012) 2019-2035
•
e-Print:
- 1112.2382
•
DOI:
- 10.1007/s10714-012-1374-z

[13]

Weak cosmic censorship, dyonic Kerr–Newman black holes and Dirac fields

Gabor Zsolt Tóth

- Class.Quant.Grav. 33 (2016) 11, 115012
•
e-Print:
- 1509.02878
•
DOI:
- 10.1088/0264-9381/33/11/115012

[14]

Grav.

C.W. Misner
,
K.S. Thorne
,
J.A. Wheeler

[15]

Applications of Lie Groups to Differential Equations

P.J. Olver

[16]

J.G. Fletcher

- Rev.Mod.Phys. 32 (1960) 65
•
DOI:
- 10.1103/RevModPhys.32.65

[17]

Noether’s second theorem and Ward identities for gauge symmetries

Steven G. Avery
(
- Brown U.
)
,
Burkhard U. W. Schwab
(
- Harvard U., Dept. Math. and
- Brown U.
)

- JHEP 02 (2016) 031
•
e-Print:
- 1510.07038
•
DOI:
- 10.1007/JHEP02(2016)031

[18]

Covariant theory of asymptotic symmetries, conservation laws and central charges

- Nucl.Phys.B 633 (2002) 3-82
•
e-Print:
- hep-th/0111246
•
DOI:
- 10.1016/S0550-3213(02)00251-1

[19]

Local BRST cohomology in gauge theories

Glenn Barnich
(
- Brussels U., PTM and
- Valencia U.
)
,
Friedemann Brandt
(
- Hannover U.
)
,
Marc Henneaux
(
- Brussels U., PTM and
- CECS, Valdivia
)

- Phys.Rept. 338 (2000) 439-569
•
e-Print:
- hep-th/0002245
•
DOI:
- 10.1016/S0370-1573(00)00049-1

[20]

S.C. Anco

e-Print:
- 1605.08734

[21]

Currents and superpotentials in classical gauge invariant theories. 1. Local results with applications to perfect fluids and general relativity

- Class.Quant.Grav. 15 (1998) 2173-2215
•
e-Print:
- gr-qc/9804029
•
DOI:
- 10.1088/0264-9381/15/8/006

[22]

Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity

- Gen.Rel.Grav. 45 (2013) 545-579
•
e-Print:
- 1211.3268
•
DOI:
- 10.1007/s10714-012-1487-4

[23]

Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. I. General Consideration

- J.Math.Phys. 54 (2013) 062504
•
e-Print:
- 1306.6887
•
DOI:
- 10.1063/1.4810017

[24]

Classical and Quantum Gravity Research

M.N. Christiansen
,
T.K. Rasmussen
,
A.N. Petrov

[25]

Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance

Friedrich W. Hehl
(
- Cologne U.
)
,
J.Dermott McCrea
(
- University Coll., Dublin and
- Dublin Inst.
)
,
Eckehard W. Mielke
(
- Cologne U.
)
,
Yuval Ne'eman
(
- Tel Aviv U. and
- Texas U.
)

- Phys.Rept. 258 (1995) 1-171
•
e-Print:
- gr-qc/9402012
•
DOI:
- 10.1016/0370-1573(94)00111-F

[26]

A General definition of 'conserved quantities' in general relativity and other theories of gravity

Robert M. Wald
(
- Chicago U., EFI and
- Chicago U.
)
,
Andreas Zoupas
(
- Chicago U., EFI and
- Chicago U.
)

- Phys.Rev.D 61 (2000) 084027
•
e-Print:
- gr-qc/9911095
•
DOI:
- 10.1103/PhysRevD.61.084027

1-25 of 57
1
2
3
25 / page