THE DEFINITION OF TIME AND QUANTUM VACUUM IN 1 + 1 DIMENSIONS

1992 ◽  
Vol 07 (25) ◽  
pp. 2317-2324 ◽  
Author(s):  
A. Z. CAPRI ◽  
S. M. ROY
Keyword(s):  
Minkowski Space ◽  
Flat Space ◽  
Space Time ◽  
Quantum Vacuum ◽  
Time Translation ◽  
Minkowski Space Time ◽  
Poincaré Symmetry ◽  
Definition Of ◽  
Field Quantization ◽  
Special Space

We prove that for any (1 + 1)-dimensional globally hyperbolic space-time it is possible to define an instant of time as a special space-like geodesic which is independent of the coordinates chosen. This definition follows uniquely from the requirement of validity of Poincaré symmetry in an infinitesimal neighborhood of the hypersurface of instantaneity. The generator associated with time translation then selects the direction of time. This fact permits unambiguous field quantization of this surface. For flat space-time the corresponding time and vacuum coincide with those of Minkowski space-time. We apply these results to static and Robertson-Walker space-times.

scholarly journals Generalized Timelike Mannheim Curves in Minkowski Space-Time

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Akyig~it ◽  
S. Ersoy ◽  
İ. Özgür ◽  
M. Tosun
Keyword(s):  
Minkowski Space ◽  
Sufficient Conditions ◽  
Space Time ◽  
Necessary And Sufficient Conditions ◽  
Minkowski Space Time ◽  
Mannheim Curve ◽  
Definition Of ◽  
Necessary And Sufficient

We give the definition of generalized timelike Mannheim curve in Minkowski space-time . The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations of generalized Mannheim curve.

scholarly journals On the structure and applications of the Bondi–Metzner–Sachs group

2018 ◽  
Vol 15 (02) ◽  
pp. 1830002 ◽  
Author(s):  
Francesco Alessio ◽  
Giampiero Esposito
Keyword(s):  
Minkowski Space ◽  
Isometry Group ◽  
Black Hole Physics ◽  
Flat Space ◽  
Space Time ◽  
Poincaré Group ◽  
Poincare Group ◽  
Curved Space ◽  
Asymptotically Flat ◽  
Minkowski Space Time

This work is a pedagogical review dedicated to a modern description of the Bondi–Metzner–Sachs (BMS) group. Minkowski space-time has an interesting and useful group of isometries, but, for a generic space-time, the isometry group is simply the identity and hence provides no significant informations. Yet symmetry groups have important role to play in physics; in particular, the Poincaré group describing the isometries of Minkowski space-time plays a role in the standard definitions of energy-momentum and angular-momentum. For this reason alone it would seem to be important to look for a generalization of the concept of isometry group that can apply in a useful way to suitable curved space-times. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work, the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of “asymptotic simplicity” are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the BMS group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the BMS group, e.g. its algebra and the possibility to obtain as its subgroup the Poincaré group, as we may expect. The paper ends with a review of the BMS invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.

COORDINATE-INDEPENDENT DEFINITION OF TIME AND VACUUM IN CURVED SPACE–TIME

1994 ◽  
Vol 09 (08) ◽  
pp. 1239-1260 ◽  
Author(s):  
A. Z. CAPRI ◽  
S. M. ROY
Keyword(s):  
Particle Production ◽  
Dimensional Space ◽  
Flat Space ◽  
Space Time ◽  
Physical Principle ◽  
De Sitter ◽  
Timelike Vector ◽  
Time Translation ◽  
Pass Through ◽  
Definition Of

We propose a definition of time and of the vacuum such that they are intrinsic to a given globally hyperbolic 1 + (n − 1)-dimensional space–time geometry and independent of the choice of coordinates. To arrive at this definition we use the new physical principle that a 1 + 1-dimensional Poincaré algebra, including Killing conditions on the generators, should be valid on the hypersurface of instantaneity. Given a timelike vector at a point (an observer's velocity) we define "an instant of time" to be the spacelike surface of geodesics which pass through that point and are orthogonal to that timelike vector. Gaussian coordinates erected on this surface yield 1 + 1-dimensional subspaces with Poincaré symmetry valid on that surface. The generator associated with time translation now uniquely picks out the direction of time on that surface. This fact permits unambiguous quantization on the surface of a field evolving in this background metric. For flat space–time the corresponding vacuum is always the Minkowski vacuum. We also consider in detail the case of static and Robertson–Walker metrics in 1 + 1 dimensions and find our vacuum to be different from those given before. The vacuum for the de Sitter metric in 1 + 1 dimensions is compared with the results in the literature and found to be different. Our definition of particles, and hence particle production, is consequently different also.

scholarly journals General Coordinatisations of the Flat Space—Time of Constant Proper-acceleration

1997 ◽  
Vol 50 (5) ◽  
pp. 851 ◽  
Author(s):  
David Tilbrook
Keyword(s):  
Minkowski Space ◽  
First Principles ◽  
Flat Space ◽  
Continuous Functions ◽  
Space Time ◽  
Frames Of Reference ◽  
Minkowski Space Time ◽  
Special Cases

We examine space-times which are described by a metric of the form ds2 = V2(X)dT2 - U2 (X)dX2 - dY2 - dZ2 in which V =V (X) and U = U(X) are continuous functions of X only and which admit diffeomorphisms into Minkowski space-time. It is shown that such space-times are associated with rigidly accelerating frames of reference by appeal to the notion of a fundamental observer. The condition for the existence of the diffeomorphism is derived from first principles and some special cases of coordinates are discussed.

scholarly journals TOPOLOGICAL REVERBERATIONS IN FLAT SPACE–TIMES

2000 ◽  
Vol 15 (26) ◽  
pp. 4141-4162 ◽  
Author(s):  
G. I. GOMERO ◽  
M. J. REBOUÇAS ◽  
A. F. F. TEIXEIRA ◽  
A. BERNUI
Keyword(s):  
Exact Solution ◽  
Minkowski Space ◽  
Explicit Solution ◽  
Radiation Reaction ◽  
Flat Space ◽  
Space Time ◽  
Reaction Equation ◽  
Spatial Direction ◽  
Multiply Connected ◽  
Minkowski Space Time

We study the role played by multiply-connectedness in the time evolution of the energy E(t) of a radiating system that lies in static flat space–time manifolds ℳ4 whose t= const spacelike sections ℳ3 are compact in at least one spatial direction. The radiation reaction equation of the radiating source is derived for the case where ℳ3 has any nontrivial flat topology, and an exact solution is obtained. We show that the behavior of the radiating energy E(t) changes remarkably from exponential damping, when the system lies in ℛ3, to a reverberation pattern (with discontinuities in the derivative Ė(t) and a set of relative minima and maxima) followed by a growth of E(t), when ℳ3 is endowed with any one of the 17 multiply-connected flat topologies. It emerges from this result that the compactness in at least one spatial direction of Minkowski space–time is sufficient to induce this type of topological reverberation, making clear that topological fragilities can arise not only in the usual cosmological modelling, but also in ordinary flat space–time manifolds. An explicit solution of the radiation reaction equation for the case where [Formula: see text] is discussed in detail, and graphs which reveal how the energy varies with the time are presented and analyzed.

On generalized partially null Mannheim curves in Minkowski space-time

2016 ◽  
Vol 46 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Emilija Nešović ◽  
Milica Grbović
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

scholarly journals CHARGED PARTICLES AND THE ELECTRO-MAGNETIC FIELD IN NONINERTIAL FRAMES OF MINKOWSKI SPACE–TIME II: "APPLICATIONS: ROTATING FRAMES, SAGNAC EFFECT, FARADAY ROTATION, WRAP-UP EFFECT"

2010 ◽  
Vol 07 (02) ◽  
pp. 185-213 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Minkowski Space ◽  
Faraday Rotation ◽  
Rotating Disk ◽  
Space Time ◽  
Sagnac Effect ◽  
Electro Magnetic Field ◽  
Minkowski Space Time ◽  
Relativistic Extension ◽  
Rotating Frames ◽  
Electro Magnetic

We apply the theory of noninertial frames in Minkowski space–time, developed in the previous paper, to various relevant physical systems. We give the 3 + 1 description without coordinate singularities of the rotating disk and the Sagnac effect, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system. Then we study properties of Maxwell equations in noninertial frames like the wrap-up effect and the Faraday rotation in astrophysics.

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

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