Abstract
We introduce a functional covariant differential as a tool for studying field space geometry in a manifestly covariant way. We then touch upon its role in gauge theories and general relativity over bounded regions, and in BRST symmetry. Due to the Gribov problem, we argue that our formalism — allowing for a non-vanishing functional curvature — is necessary for a global treatment of gauge-invariance in field space. We conclude by suggesting that the structures we introduce satisfactorily implement the notion of a (non-asymptotic) observer in gauge theories and general relativity.
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References
J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].
H. de A. Gomes, Classical gauge theory in Riem, J. Math. Phys. 52 (2011) 082501 [arXiv:0807.4405] [INSPIRE].
H. Gomes, A geodesic model in conformal superspace, to appear.
G. Vilkovisky, The gospel according to DeWitt, in Quantum theory of gravity: essays in honor of the 60th birthday of Bryce S. DeWitt, S.M. Christensen ed. (1984) [INSPIRE].
B.S. DeWitt and C. Molina-Paris, Quantum gravity without ghosts, Mod. Phys. Lett. A 13 (1998) 2475 [hep-th/9808163] [INSPIRE].
P. Cotta-Ramusino and C. Reina, The action of the group of bundle-automorphisms on the space of connections and the geometry of gauge theories, J. Geom. Phys. 1N3 (1984) 121 [INSPIRE].
J.M. Pawlowski, Geometrical effective action and Wilsonian flows, hep-th/0310018 [INSPIRE].
I. Donkin and J.M. Pawlowski, The phase diagram of quantum gravity from diffeomorphism-invariant RG-flows, arXiv:1203.4207 [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. 37B (1971) 95 [INSPIRE].
B. Zumino, Y.-S. Wu and A. Zee, Chiral Anomalies, Higher Dimensions and Differential Geometry, Nucl. Phys. B 239 (1984) 477 [INSPIRE].
Y.-S. Wu, Descent equations, gauge structure in configuration space and topology of quantum field theory, (2015) http://pirsa.org/15100100.
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
M. Campiglia and A. Laddha, Sub-subleading soft gravitons: New symmetries of quantum gravity?, Phys. Lett. B 764 (2017) 218 [arXiv:1605.09094] [INSPIRE].
W. Donnelly and L. Freidel, Local subsystems in gauge theory and gravity, JHEP 09 (2016) 102 [arXiv:1601.04744] [INSPIRE].
F. Hopfmüller, Null boundaries in covariant Hamiltonian general relativity, MSc Thesis, Perimeter Scholar International, Perimeter Institute (2016).
V.N. Gribov, Instability of non-Abelian gauge theories and impossibility of choice of Coulomb gauge, SLAC-TRANS-0176 (1977) [INSPIRE].
I.M. Singer, Some Remarks on the Gribov Ambiguity, Commun. Math. Phys. 60 (1978) 7 [INSPIRE].
S. Lang, Fundamentals of Differential Geometry, Graduate Texts in Mathematics 191 (1999), Springer New York, New York, NY [ISBN: 978-1-4612-6810-9].
A. Kriegl and P.W. Michor, The Convenient Setting of Global Analysis, Mathematical Surveys and Monographs (1997).
L. Bonora and P. Cotta-Ramusino, Some Remarks on BRS Transformations, Anomalies and the Cohomology of the Lie Algebra of the Group of Gauge Transformations, Commun. Math. Phys. 87 (1983) 589 [INSPIRE].
R.A. Bertlmann, Anomalies in Quantum Field Theory, Oxford University Press (2000) [ISBN 9780198507628].
Z. Jaskólski, The Integration of G Invariant Functions and the Geometry of the Faddeev-popov Procedure, Commun. Math. Phys. 111 (1987) 439 [INSPIRE].
I.A. Batalin and G.A. Vilkovisky, Gauge Algebra and Quantization, Phys. Lett. B 102 (1981) 27 [INSPIRE].
A. Cattaneo, P. Mnev and N. Reshetikhin, Classical BV theories on manifolds with boundary, Commun. Math. Phys. 332 (2014) 535 [arXiv:1201.0290] [INSPIRE].
D. Zwanziger, Local and Renormalizable Action From the Gribov Horizon, Nucl. Phys. B 323 (1989) 513 [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
T. He, P. Mitra and A. Strominger, 2D Kac-Moody Symmetry of 4D Yang-Mills Theory, JHEP 10 (2016) 137 [arXiv:1503.02663] [INSPIRE].
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105 (2010) 111103 [arXiv:0909.2617] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
M. Campiglia and A. Laddha, Sub-subleading soft gravitons: New symmetries of quantum gravity?, Phys. Lett. B 764 (2017) 218 [arXiv:1605.09094] [INSPIRE].
C. Rovelli, Why Gauge?, Found. Phys. 44 (2014) 91.
J. Barbour, B.Z. Foster and N. O’Murchadha, Relativity without relativity, Class. Quant. Grav. 19 (2002) 3217 [gr-qc/0012089] [INSPIRE].
F. Mercati, A Shape Dynamics Tutorial, arXiv:1409.0105 [INSPIRE].
R.G. Littlejohn and M. Reinsch, Gauge fields in the separation of rotations and internal motions in the N body problem, Rev. Mod. Phys. 69 (1997) 213 [INSPIRE].
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Gomes, H., Riello, A. The observer’s ghost: notes on a field space connection. J. High Energ. Phys. 2017, 17 (2017). https://doi.org/10.1007/JHEP05(2017)017
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DOI: https://doi.org/10.1007/JHEP05(2017)017