Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

We review what is known about boundary conditions in General Relativity on a spacetime of Euclidean signature. The obvious Dirichlet boundary condition, in which one specifies the boundary geometry, is actually not elliptic and in general does not lead to a well-defined perturbation theory. It is better-behaved if the extrinsic curvature of the boundary is suitably constrained, for instance if it is positive- or negative-definite. A different boundary condition, in which one specifies the conformal geometry of the boundary and the trace of the extrinsic curvature, is elliptic and always leads formally to a satisfactory perturbation theory. These facts might have interesting implications for semiclassical approaches to quantum gravity. April, 2018

Download Full-text

Exorcising ghosts in quantum gravity

The European Physical Journal Plus ◽

10.1140/epjp/s13360-020-00875-x ◽

2020 ◽

Vol 135 (10) ◽

Author(s):

Iberê Kuntz

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Gravity ◽

Boundary Conditions ◽

Finite Number ◽

Integration Contour ◽

Quantum Field ◽

Curvature Invariants ◽

Higher Derivative ◽

Quadratic Gravity

AbstractWe remark that Ostrogradsky ghosts in higher-derivative gravity, with a finite number of derivatives, are fictitious as they result from an unjustified truncation performed in a complete theory containing infinitely many curvature invariants. The apparent ghosts can then be projected out of the quadratic gravity spectrum by redefining the boundary conditions of the theory in terms of an integration contour that does not enclose the ghost poles. This procedure does not alter the renormalizability of the theory. One can thus use quadratic gravity as a quantum field theory of gravity that is both renormalizable and unitary.

Download Full-text

A FIELD THEORETICAL APPROACH FOR STRINGS AND INTERFACES OF ISING-LIKE MODELS AT d>1

International Journal of Modern Physics B ◽

10.1142/s0217979296001094 ◽

1996 ◽

Vol 10 (18n19) ◽

pp. 2431-2440

Author(s):

M. MARTELLINI ◽

M. SPREAFICO ◽

K. YOSHIDA

Keyword(s):

Quantum Gravity ◽

Boundary Conditions ◽

Numerical Simulations ◽

Theoretical Approach ◽

Critical Exponents ◽

Polymer Phase ◽

Random Surface ◽

Surface Models ◽

D Values ◽

Physical Boundary

Starting from a generalized version of David-Distler-Kawai treatment of 2d-induced quantum gravity, we impose a series of “physical” boundary conditions to obtain an unique field theoretical Lagrangian describing random surface models and strings at given dimensions d>1. Our theory reproduces the critical exponents obtained by numerical simulations on d-dimensional Ising-like models for lower d-values. One observes, at appropriate dimensions d, the transition to the so-called branched polymer phase.

Download Full-text

Exact spectral asymptotics for the Laplace - Beltrami operator in the case of general elliptic boundary conditions

Functional Analysis and Its Applications ◽

10.1007/bf01082382 ◽

1981 ◽

Vol 15 (1) ◽

pp. 59-60 ◽

Cited By ~ 1

Author(s):

V. Ya. Ivrii

Keyword(s):

Boundary Conditions ◽

Elliptic Boundary ◽

Beltrami Operator ◽

Spectral Asymptotics ◽

General Elliptic ◽

General Elliptic Boundary

Download Full-text

Spectral asymptotics and basis properties of fourth order differential operators with regular boundary conditions

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.2827 ◽

2013 ◽

Vol 37 (5) ◽

pp. 698-710 ◽

Cited By ~ 2

Author(s):

Nazim B. Kerimov ◽

Ufuk Kaya

Keyword(s):

Boundary Conditions ◽

Fourth Order ◽

Differential Operators ◽

Spectral Asymptotics ◽

Regular Boundary ◽

Regular Boundary Conditions

Download Full-text

Time-space duality in 2D quantum gravity

Classical and Quantum Gravity ◽

10.1088/1361-6382/ac4615 ◽

2021 ◽

Author(s):

Ding Jia

Keyword(s):

Quantum Gravity ◽

Boundary Conditions ◽

Path Integral ◽

Local Symmetry ◽

Important Task ◽

Causal Relations ◽

Time Space ◽

Equal Amplitude

Abstract An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global Z2 symmetry of 1+1D quantum gravity, we show that gravitational path integral conﬁgurations come in equal amplitude pairs with timelike and spacelike relations exchanged. As a consequence, any two points are equally probable to be timelike and spacelike separated in a universe without boundary conditions. In the context of simplicial quantum gravity we identify a local symmetry of the action which shows that even with boundary conditions causal uncertainties are generically present. Depending on the boundary conditions, causal uncertainties can still be large and even maximal.

Download Full-text