QUANTUM CYLINDRICAL WAVES AND PARAMETRIZED FIELD THEORY

2006 ◽  
Vol 15 (10) ◽  
pp. 1743-1752 ◽  
Author(s):  
MADHAVAN VARADARAJAN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Flat Space ◽  
Space Time ◽  
Gravitational Fields ◽  
Cylindrical Waves ◽  
Cylindrically Symmetric ◽  
Gravity Effects ◽  
Free Scalar

In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space–time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space–time and review the relevant results for unitary implementability.

scholarly journals FIELD THEORY ON κ-MINKOWSKI SPACE REVISITED: NOETHER CHARGES AND BREAKING OF LORENTZ SYMMETRY

2008 ◽  
Vol 23 (18) ◽  
pp. 2687-2718 ◽  
Author(s):  
LAURENT FREIDEL ◽  
JERZY KOWALSKI-GLIKMAN ◽  
SEBASTIAN NOWAK
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Minkowski Space ◽  
Lorentz Invariance ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Field Equations ◽  
Conserved Charges ◽  
Lorentz Scalar ◽  
Free Scalar

This paper is devoted to detailed investigations of free scalar field theory on κ-Minkowski space. After reviewing necessary mathematical tools, we discuss in detail the Lagrangian and solutions of field equations. We analyze the space–time symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetries. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: there is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.

scholarly journals LARGE QUANTUM GRAVITY EFFECTS: CYLINDRICAL WAVES IN FOUR DIMENSIONS

2000 ◽  
Vol 09 (06) ◽  
pp. 669-686 ◽  
Author(s):  
MARÍA E. ANGULO ◽  
GUILLERMO A. MENA MARUGÁN
Keyword(s):  
Quantum Gravity ◽  
Symmetry Axis ◽  
Point Of View ◽  
Three Dimensions ◽  
Asymptotic Region ◽  
Four Dimensions ◽  
Cylindrical Waves ◽  
Significant Difference ◽  
Gravity Effects ◽  
Linearly Polarized

Linearly polarized cylindrical waves in four-dimensional vacuum gravity are mathematically equivalent to rotationally symmetric gravity coupled to a Maxwell (or Klein–Gordon) field in three dimensions. The quantization of this latter system was performed by Ashtekar and Pierri in a recent work. Employing that quantization, we obtain here a complete quantum theory which describes the four-dimensional geometry of the Einstein–Rosen waves. In particular, we construct regularized operators to represent the metric. It is shown that the results achieved by Ashtekar about the existence of important quantum gravity effects in the Einstein–Maxwell system at large distances from the symmetry axis continue to be valid from a four-dimensional point of view. The only significant difference is that, in order to admit an approximate classical description in the asymptotic region, states that are coherent in the Maxwell field need not contain a large number of photons anymore. We also analyze the metric fluctuations on the symmetry axis and argue that they are generally relevant for all of the coherent states.

scholarly journals Free Scalar Fields in Finite Volume Are Holographic

Universe ◽  
2019 ◽  
Vol 5 (12) ◽  
pp. 223
Author(s):  
Csaba Balázs
Keyword(s):  
Scalar Field ◽  
Surface Area ◽  
Finite Volume ◽  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Flat Space ◽  
Linear Size ◽  
Energy Mode ◽  
Free Scalar ◽  
Quantized Field

This brief note presents a back-of-the-envelope calculation showing that the number of degrees of freedom of a free scalar field in expanding flat space equals the surface area of the Hubble volume in Planck units. The logic of the calculation is the following. The amount of energy in the Hubble volume scales with its linear size, consequently the volume can only contain a finite number of quantized field modes. Since the momentum of the lowest energy mode scales inversely with the linear size of the volume, the maximal number of such modes in the volume scales with its surface area. It is possible to show that when the number of field modes is saturated the modes are confined to the surface of the volume. Gravity only enters this calculation as a regulator, providing a finite volume that contains the field, the entire calculation is done in flat space. While this toy model is bound to be incomplete, it is potentially interesting because it reproduces the defining aspects of holography, and advocates a regularization of the quantum degrees of freedom based on Friedmann’s equation.

scholarly journals SPECTRAL GEOMETRY AND CAUSALITY

1998 ◽  
Vol 13 (15) ◽  
pp. 2693-2708 ◽  
Author(s):  
TOMÁŠ KOPF
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Spectral Data ◽  
Physical Interpretation ◽  
Lorentzian Manifold ◽  
Space Time ◽  
Effective Field ◽  
Spectral Geometry ◽  
Causal Relationships ◽  
Classical Space

For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical space–time, at least approximately. However, quantum gravity may eventually provide classical space–times by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a space–time manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of histories.

Time, Topology, and the Twin Paradox

2011 ◽  
Author(s):  
Jean‐Pierre Luminet
Keyword(s):  
High Speed ◽  
Reference Frames ◽  
Thought Experiment ◽  
Flat Space ◽  
Space Time ◽  
Twin Paradox ◽  
Theory Of Relativity ◽  
Apparent Paradox ◽  
Curved Space ◽  
Gravitational Fields

This chapter notes that the twin paradox is the best-known thought experiment associated with Einstein's theory of relativity. An astronaut who makes a journey into space in a high-speed rocket will return home to find he has aged less than his twin who stayed on Earth. This result appears puzzling, as the homebody twin can be considered to have done the travelling with respect to the traveller. Hence, it is called a “paradox”. In fact, there is no contradiction, and the apparent paradox has a simple resolution in special relativity with infinite flat space. In general relativity (dealing with gravitational fields and curved space-time), or in a compact space such as the hypersphere or a multiply connected finite space, the paradox is more complicated, but its resolution provides new insights about the structure of space–time and the limitations of the equivalence between inertial reference frames.

scholarly journals GLOBAL MONOPOLES AND SCALAR FIELDS AS THE ELECTROGRAVITY DUAL OF SCHWARZSCHILD SPACE–TIME

2001 ◽  
Vol 16 (18) ◽  
pp. 1193-1200 ◽  
Author(s):  
NARESH DADHICH ◽  
NARAYAN BANERJEE
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Scalar Fields ◽  
Flat Space ◽  
Space Time ◽  
Global Monopole ◽  
Schwarzschild Solution ◽  
State Formula ◽  
Global Monopoles ◽  
First Time

We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, [Formula: see text]. This property was however known for the global monopole space–time while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos–Zannias scalar field solution is dual to flat space.

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