On the energy-momentum tensor in Moyal space

Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; Schweda, Manfred

doi:10.1140/epjc/s10052-015-3492-8

On the energy-momentum tensor in Moyal space

Journal Article · Fri Jun 26 00:00:00 EDT 2015 · European Physical Journal. C, Particles and Fields

DOI:https://doi.org/10.1140/epjc/s10052-015-3492-8· OSTI ID:1221372

Balasin, Herbert ^[1]; Blaschke, Daniel N. ^[2]; Gieres, François ^[3]; Schweda, Manfred ^[1]

Vienna Univ. of Technology (Austria). Inst. of Theoretical Physics
Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theory Division
Inst. de Physique Nucleaire de Lyon (IPNL), Villeurbanne (France)

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another starproduct. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1221372

Alternate ID(s):: OSTI ID: 22387236

Report Number(s):: LA-UR--15-21030; PII: 3492

Journal Information:: European Physical Journal. C, Particles and Fields, Journal Name: European Physical Journal. C, Particles and Fields Journal Issue: 6 Vol. 75; ISSN 1434-6044

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (40)

A Translation-Invariant Renormalizable Non-Commutative Scalar Model Gurau, R.; Magnen, J.; Rivasseau, V. Communications in Mathematical Physics, Vol. 287, Issue 1 https://doi.org/10.1007/s00220-008-0658-3	journal	October 2008
Brane compactifications and 4-dimensional geometry in the IKKT model Polychronakos, Alexios P.; Steinacker, Harold; Zahn, Jochen Nuclear Physics B, Vol. 875, Issue 3 https://doi.org/10.1016/j.nuclphysb.2013.07.017	journal	October 2013
Chiral gauge anomalies on noncommutative Gracia-Bondı́a, J. M.; Martı́n, C. P. Physics Letters B, Vol. 479, Issue 1-3 https://doi.org/10.1016/s0370-2693(00)00344-0	journal	April 2000
Comments on the energy–momentum tensor in non-commutative field theories Abou-Zeid, Mohab; Dorn, Harald Physics Letters B, Vol. 514, Issue 1-2 https://doi.org/10.1016/s0370-2693(01)00780-8	journal	August 2001
The IR/UV connection in the non-commutative gauge theories Matusis, Alec; Susskind, Leonard; Toumbas, Nicolaos Journal of High Energy Physics, Vol. 2000, Issue 12 https://doi.org/10.1088/1126-6708/2000/12/002	journal	December 2000
Noncommutative Φ ⁴ theory at two loops Micu, Andrei; Sheikh-Jabbari, Mohammad M. Journal of High Energy Physics, Vol. 2001, Issue 01 https://doi.org/10.1088/1126-6708/2001/01/025	journal	January 2001
Gauge Theories on Deformed Spaces Blaschke, Daniel N. Symmetry, Integrability and Geometry: Methods and Applications https://doi.org/10.3842/sigma.2010.062	journal	August 2010
Classical Noncommutative Electrodynamics with External Source Adorno, T. C.; Gitman, D. M.; Shabad, A. E. arXiv https://doi.org/10.48550/arxiv.1106.0639	text	January 2011
Wong's Equations and Charged Relativistic Particles in Non-Commutative Space Balasin, Herbert; Blaschke, Daniel N.; Gieres, Francois arXiv https://doi.org/10.48550/arxiv.1403.0255	text	January 2014
Wess-Zumino-Witten and fermion models in noncommutative space Moreno, E. F.; Schaposnik, F. A. arXiv https://doi.org/10.48550/arxiv.hep-th/0008118	text	January 2000
On the unitarity problem in space/time noncommutative theories Bahns, D.; Doplicher, S.; Fredenhagen, K. arXiv https://doi.org/10.48550/arxiv.hep-th/0201222	text	January 2002
Discrete-Time Quantum Field Theory and the Deformed Super Virasoro Algebra Chaichian, Masud; Presnajder, Peter arXiv https://doi.org/10.48550/arxiv.hep-th/0209024	text	January 2002
Non-commutative Renormalization Rivasseau, Vincent Quantum Spaces. Progress in Mathematical Physics https://doi.org/10.1007/978-3-7643-8522-4_2	book	January 2007
Renormalisation of ?4-Theory on Noncommutative ?4 in the Matrix Base Grosse, Harald; Wulkenhaar, Raimar Communications in Mathematical Physics, Vol. 256, Issue 2 https://doi.org/10.1007/s00220-004-1285-2	journal	February 2005
Self-Dual Noncommutative $${\phi^4}$$ ϕ 4 -Theory in Four Dimensions is a Non-Perturbatively Solvable and Non-Trivial Quantum Field Theory Grosse, Harald; Wulkenhaar, Raimar Communications in Mathematical Physics, Vol. 329, Issue 3 https://doi.org/10.1007/s00220-014-1906-3	journal	March 2014
On the principles of elementary quantum mechanics Groenewold, H. J. Physica, Vol. 12, Issue 7 https://doi.org/10.1016/S0031-8914(46)80059-4	journal	October 1946
Quantum field theory on noncommutative spaces Szabo, R. Physics Reports, Vol. 378, Issue 4 https://doi.org/10.1016/S0370-1573(03)00059-0	journal	May 2003
Perturbative analysis on infrared aspects of noncommutative QED on R4 Hayakawa, M. Physics Letters B, Vol. 478, Issue 1-3 https://doi.org/10.1016/S0370-2693(00)00242-2	journal	April 2000
Chiral gauge anomalies on noncommutative Gracia-Bondı́a, J. M.; Martı́n, C. P. Physics Letters B, Vol. 479, Issue 1-3 https://doi.org/10.1016/S0370-2693(00)00344-0	journal	April 2000
Comments on the energy–momentum tensor in non-commutative field theories Abou-Zeid, Mohab; Dorn, Harald Physics Letters B, Vol. 514, Issue 1-2 https://doi.org/10.1016/S0370-2693(01)00780-8	journal	August 2001
Noncommutative gauge field theories: a no-go theorem Chaichian, M.; Prešnajder, P.; Sheikh-Jabbari, M. M. Physics Letters B, Vol. 526, Issue 1-2 https://doi.org/10.1016/S0370-2693(01)01478-2	journal	January 2002
On the unitarity problem in space/time noncommutative theories Bahns, D.; Doplicher, S.; Fredenhagen, K. Physics Letters B, Vol. 533, Issue 1-2 https://doi.org/10.1016/S0370-2693(02)01563-0	journal	May 2002
Wess–Zumino–Witten and fermion models in noncommutative space Moreno, E. F.; Schaposnik, F. A. Nuclear Physics B, Vol. 596, Issue 1-2 https://doi.org/10.1016/S0550-3213(00)00702-1	journal	February 2001
-Trek: the one-loop noncommutative SYM action Liu, Hong; Michelson, Jeremy Nuclear Physics B, Vol. 614, Issue 1-2 https://doi.org/10.1016/S0550-3213(01)00401-1	journal	October 2001
Renormalization of the energy–momentum tensor in non-commutative scalar field theory Bellucci, S.; Buchbinder, I. L.; Krykhtin, V. A. Nuclear Physics B, Vol. 665 https://doi.org/10.1016/S0550-3213(03)00463-2	journal	August 2003
Wilson loops in non-commutative Yang–Mills Ishibashi, Nobuyuki; Iso, Satoshi; Kawai, Hikaru Nuclear Physics B, Vol. 573, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00708-7	journal	May 2000
Emergent gravity and noncommutative branes from Yang–Mills matrix models Steinacker, Harold Nuclear Physics B, Vol. 810, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2008.10.014	journal	March 2009
Quantum mechanics as a statistical theory Moyal, J. E. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 45, Issue 1 https://doi.org/10.1017/S0305004100000487	journal	January 1949
Wick rotation for quantum field theories on degenerate Moyal space(-time) Grosse, Harald; Lechner, Gandalf; Ludwig, Thomas Journal of Mathematical Physics, Vol. 54, Issue 2 https://doi.org/10.1063/1.4790886	journal	February 2013
Noncommutative perturbative dynamics Minwalla, Shiraz; Raamsdonk, Mark Van; Seiberg, Nathan Journal of High Energy Physics, Vol. 2000, Issue 02 https://doi.org/10.1088/1126-6708/2000/02/020	journal	February 2000
Generalized *-products, Wilson lines and the solution of the Seiberg-Witten equations Mehen, Thomas; Wise, Mark B. Journal of High Energy Physics, Vol. 2000, Issue 12 https://doi.org/10.1088/1126-6708/2000/12/008	journal	December 2000
Renormalisation of phi ⁴ -theory on noncommutative Bbb R ² in the matrix base Grosse, Harald; Wulkenhaar, Raimar Journal of High Energy Physics, Vol. 2003, Issue 12 https://doi.org/10.1088/1126-6708/2003/12/019	journal	December 2003
Classical Yang-Mills theory in the presence of external sources Sikivie, P.; Weiss, N. Physical Review D, Vol. 18, Issue 10 https://doi.org/10.1103/PhysRevD.18.3809	journal	November 1978
Remarks on the noncommutative Wess-Zumino model Pengpan, Teparksorn; Xiong, Xiaozhen Physical Review D, Vol. 63, Issue 8 https://doi.org/10.1103/PhysRevD.63.085012	journal	March 2001
Energy-momentum tensor in noncommutative gauge theories Das, Ashok; Frenkel, J. Physical Review D, Vol. 67, Issue 6 https://doi.org/10.1103/PhysRevD.67.067701	journal	March 2003
Classical noncommutative electrodynamics with external source Adorno, T. C.; Gitman, D. M.; Shabad, A. E. Physical Review D, Vol. 84, Issue 6 https://doi.org/10.1103/PhysRevD.84.065003	journal	September 2011
The photon-neutrino interaction induced by non-commutativity and astrophysical bounds Schupp, P.; Trampetić, J.; Wess, J. The European Physical Journal C, Vol. 36, Issue 3 https://doi.org/10.1140/epjc/s2004-01874-5	journal	August 2004
The Energy–Momentum Tensor in Noncommutative Gauge Field Models Grimstrup, J. M.; KloibÖCk, B.; Popp, L. International Journal of Modern Physics A, Vol. 19, Issue 32 https://doi.org/10.1142/S0217751X04021007	journal	December 2004
Gauge Theories on Deformed Spaces Blaschke, Daniel N. Symmetry, Integrability and Geometry: Methods and Applications https://doi.org/10.3842/SIGMA.2010.062	journal	August 2010
Wong's Equations and Charged Relativistic Particles in Non-Commutative Space Balasin, Herbert Symmetry, Integrability and Geometry: Methods and Applications https://doi.org/10.3842/SIGMA.2014.099	journal	October 2014

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Energy momentum tensor for translation invariant renormalizable noncommutative field theory Baloïtcha, Ezinvi; Lahoche, Vincent; Samary, Dine Ousmane The European Physical Journal Plus, Vol. 133, Issue 12 https://doi.org/10.1140/epjp/i2018-12339-8	journal	December 2018
Aspects of perturbative quantum field theory on non-commutative spaces Blaschke, Daniel Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015) https://doi.org/10.22323/1.263.0104	conference	November 2016
Field Theory with Coordinate Dependent Noncommutativity Blaschke, Daniel N.; Gieres, Francois Symmetry, Integrability and Geometry: Methods and Applications https://doi.org/10.3842/sigma.2018.133	journal	December 2018

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