Influence of the Path Integral Measure in Quantum Gravity

1997 ◽  
pp. 417-417
Author(s):  
Christian Holm
Keyword(s):  
Quantum Gravity ◽  
Path Integral ◽  
Integral Measure

scholarly journals Topological violation of global symmetries in quantum gravity

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Kazuya Yonekura
Keyword(s):  
Quantum Gravity ◽  
Global Symmetries ◽  
Gauge Field ◽  
Path Integral ◽  
Black Brane ◽  
Current Conservation ◽  
Charge Conservation ◽  
Local Current ◽  
Topological Construction ◽  
Breaking Term

Abstract We discuss a topological reason why global symmetries are not conserved in quantum gravity, at least when the symmetry comes from compactification of a higher form symmetry. The mechanism is purely topological and does not require any explicit breaking term in the UV Lagrangian. Local current conservation does not imply global charge conservation in a sum over geometries in the path integral. We explicitly consider the shift symmetry of an axion-like field which originates from the compactification of a p-form gauge field. Our topological construction is motivated by the brane/black-brane correspondence, brane instantons, and an idea that virtual black branes of a simple kind may be realized by surgery on spacetime manifolds.

scholarly journals ABELIAN ANOMALIES IN NONLOCAL REGULARIZATION

1994 ◽  
Vol 09 (26) ◽  
pp. 4549-4564 ◽  
Author(s):  
M.A. CLAYTON ◽  
L. DEMOPOULOS ◽  
J.W. MOFFAT
Keyword(s):  
Path Integral ◽  
Invariant Theory ◽  
Axial Anomaly ◽  
Regularization Scheme ◽  
Integral Measure ◽  
Nonlocal Regularization ◽  
Noether Current

The nonlocal regularization of QED is shown to possess an axial anomaly of the same form as other regularization schemes. The Noether current is explicitly constructed and the symmetries are shown to be violated, whereas the identities constructed when one properly considers the contribution from the path integral measure are respected. We also discuss the merits and new features of the regularization scheme, as well as the barrier to quantizing the fully gauged chiral-invariant theory.

scholarly journals An alternative path integral for quantum gravity

2016 ◽  
Vol 2016 (10) ◽  
Author(s):  
Chethan Krishnan ◽  
K. V. Pavan Kumar ◽  
Avinash Raju
Keyword(s):  
Quantum Gravity ◽  
Path Integral ◽  
Alternative Path

PATH INTEGRAL ON THE EXTREME FIELD CONFIGURATIONS

2011 ◽  
Vol 26 (01) ◽  
pp. 135-148
Author(s):  
V. M. KHATSYMOVSKY
Keyword(s):  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Tangential Component ◽  
Generalized Function ◽  
Time Axis ◽  
Generalized Coordinates ◽  
Fast Change ◽  
Integral Measure ◽  
Gravity System

The canonical Hamiltonian path integral measure obeys certain rule which relates such measure on the paths defined on the whole time axis to the measures on the paths defined on the regions constituting the time axis. We show that this "gluing" rule can be reproduced without referring to Hamiltonian formalism, by substituting field configurations with arbitrarily fast change of the fields at the boundary points of these regions into action and viewing the path integral in the sense of generalized function. Now the coordinate along which gluing proceeds can be not only the time. The piecewise-flat (simplicial) minisuperspace gravity system is considered. Arbitrarily fast change of the (tangential component of) metric between the two 4-simplices with common 3-face is studied. That is, we generalize piecewise-flat anzats by allowing tangential metric to be function of the distance from the 3-face in the neighborhood of this 3-face. The action is nondegenerate (nonsingular) with respect to these additional generalized coordinates. The rule for gluing the path integral measures on separate 4-simplices is found. The resulting general expression covers a large variety of the measures including those usually used in numerical calculations and allows one to specify the measure in some applications.

Path-integral and operator formalism in quantum gravity

1987 ◽  
Vol 35 (8) ◽  
pp. 2309-2314 ◽  
Author(s):  
H. Arisue ◽  
T. Fujiwara ◽  
M. Kato ◽  
K. Ogawa
Keyword(s):  
Quantum Gravity ◽  
Path Integral ◽  
Operator Formalism

scholarly journals SPIN-STATISTICS THEOREM IN PATH INTEGRAL FORMULATION

2001 ◽  
Vol 16 (24) ◽  
pp. 4025-4044 ◽  
Author(s):  
KAZUO FUJIKAWA
Keyword(s):  
Path Integral ◽  
Energy Condition ◽  
Integral Formulation ◽  
Positive Energy ◽  
Path Integral Formulation ◽  
Dimensional Theory ◽  
Scalar Particles ◽  
Dirac Particles ◽  
Integral Measure ◽  
Local Path

We present a coherent proof of the spin-statistics theorem in path integral formulation. The local path integral measure and Lorentz-invariant local Lagrangian, when combined with the Green functions defined in terms of time ordered products, ensure causality regardless of statistics. The Feynman m-iε prescription ensures the positive energy condition regardless of statistics, and the abnormal spin-statistics relation for both the spin-0 scalar particles and spin-1/2 Dirac particles is excluded if one imposes the positive norm condition in conjunction with Schwinger's action principle. The minus commutation relation between one Bose and one Fermi field arises naturally in the path integral. The Feynman m-iε prescription also ensures a smooth continuation to Euclidean theory, for which the use of the Weyl anomaly is illustrated to exclude the abnormal statistics for the scalar and Dirac particles not only in four-dimensional theory but also in two-dimensional theory.

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