scholarly journals BOSONIC STRING THEORY IN BACKGROUND FIELDS BY CANONICAL METHODS

2005 ◽  
Vol 20 (23) ◽  
pp. 5501-5512 ◽  
Author(s):  
B. SAZDOVIĆ
Keyword(s):  
Energy Momentum Tensor ◽  
Curve Space ◽  
Momentum Tensor ◽  
Space Time ◽  
Bosonic String ◽  
General Covariance ◽  
Classical Dynamics ◽  
Background Fields ◽  
Curve Space Time ◽  
Opposite Chirality

We investigate classical dynamics of the bosonic string in the background metric, antisymmetric and dilaton fields. We use canonical methods to find Hamiltonian in terms of energy–momentum tensor components. The later are secondary constraints of the theory. Due to the presence of the dilaton field the Virasoro generators have nonlinear realization. We find that, in the curve space–time, opposite chirality currents do not commute. As a consequence of the two-dimensional general covariance, the energy–momentum tensor components satisfy two Virasoro algebras, even in the curve space–time. We emphasize that background antisymmetric and dilaton fields are the origin of space–time torsion and space–time nonmetricity, respectively.

scholarly journals Theory of Spinors in Curved Space-Time

2020 ◽  
Author(s):  
Ying-Qiu Gu
Keyword(s):  
Clifford Algebra ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Classical Dynamics ◽  
Curved Space ◽  
Spinor Fields ◽  
Classical Approximation ◽  
Dirac Matrix ◽  
Spinor Connection

The interaction between spinors and gravity is the most complicated and subtle interaction in the universe, which involves the basic problem to unified quantum theory and general relativity. By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of Dirac equation, the energy momentum tensor of spinors and so on. To split spinor connection into Keller connection $\Upsilon_\mu\in\Lambda^1$ and pseudo-vector potential $\Omega_\mu\in\Lambda^3$ by Clifford algebra not only makes the calculation simpler, but also highlights their different physical meanings. The representation of the new spinor connection is dependent only on the metric, but not on the Dirac matrix. Keller connection only corresponds to geometric calculations, but the potential $\Omega_\mu$ has dynamical effects, which couples with the spin of a spinor and may be the origin of the celestial magnetic field. Only in the new form of connection can we clearly define the classical concepts for the spinor field and then derive its complete classical dynamics, that is, Newton's second law of particles. To study the interaction between space-time and fermion, we need an explicit form of the energy-momentum tensor of spinor fields. However, the energy-momentum tensor is closely related to the tetrad, and the tetrad cannot be uniquely determined by the metric. This uncertainty increases the difficulty of deriving rigorous expression. In this paper, through a specific representation of tetrad, we derive the concrete energy-momentum tensor and its classical approximation. In the derivation of energy-momentum tensor, we obtain a spinor coefficient table $S^{\mu\nu}_{ab}$, which plays an important role in the interaction between spinor and gravity. From this paper we find that, Clifford algebra has irreplaceable advantages in the study of geometry and physics.

scholarly journals Theory of Spinors in Curved Space-Time

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1931
Author(s):  
Ying-Qiu Gu
Keyword(s):  
Clifford Algebra ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Classical Dynamics ◽  
Curved Space ◽  
Spinor Fields ◽  
Classical Approximation ◽  
Dirac Matrix ◽  
Spinor Connection

By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of the Dirac equation, the energy-momentum tensor of spinors and so on. To split the spinor connection into the Keller connection Υμ∈Λ1 and the pseudo-vector potential Ωμ∈Λ3 not only makes the calculation simpler, but also highlights their different physical meanings. The representation of the new spinor connection is dependent only on the metric, but not on the Dirac matrix. Only in the new form of connection can we clearly define the classical concepts for the spinor field and then derive its complete classical dynamics, that is, Newton’s second law of particles. To study the interaction between space-time and fermion, we need an explicit form of the energy-momentum tensor of spinor fields; however, the energy-momentum tensor is closely related to the tetrad, and the tetrad cannot be uniquely determined by the metric. This uncertainty increases the difficulty of deriving rigorous expression. In this paper, through a specific representation of tetrad, we derive the concrete energy-momentum tensor and its classical approximation. In the derivation of energy-momentum tensor, we obtain a spinor coefficient table Sabμν, which plays an important role in the interaction between spinor and gravity. From this paper we find that Clifford algebra has irreplaceable advantages in the study of geometry and physics.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

scholarly journals Positive Energy Driven CTCs In ADM 3+1 Space – Time of Unprotected Chronology

2021 ◽  
Author(s):  
Deep Bhattacharjee
Keyword(s):  
Energy Density ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Exotic Matter ◽  
Positive Energy ◽  
Spacelike Hypersurfaces ◽  
Stress Energy ◽  
Maxwell Fields ◽  
Stress Energy Momentum Tensor

Chronology unprotected mechanisms are considered with a very low gravitational polarization to make the wormhole traversal with positive energy density everywhere. No need of exotic matter has been considered with the assumption of the Einstein-Dirac-Maxwell Fields, encountering above the non-zero stress-energy-momentum tensor through spacelike hypersurfaces by a hyperbolic coordinate shift.

QUANTIZATION OF THE LIOUVILLE MODE AND STRING THEORY

1989 ◽  
Vol 04 (11) ◽  
pp. 1033-1041 ◽  
Author(s):  
SUMIT R. DAS ◽  
SATCHIDANANDA NAIK ◽  
SPENTA R. WADIA
Keyword(s):  
String Theory ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Two Dimensions ◽  
General Covariance ◽  
World Sheet ◽  
Lorentzian Signature ◽  
Dimensional Space Time ◽  
Background Fields

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

scholarly journals Klein Gordon Field in FLRW Space-Time

2020 ◽  
Vol 13 (13) ◽  
pp. 1-4
Author(s):  
S.K. Sharma ◽  
P.R. Dhungel ◽  
U. Khanal
Keyword(s):  
Spherical Harmonics ◽  
Energy Momentum Tensor ◽  
Equation Of Motion ◽  
Momentum Tensor ◽  
Space Time ◽  
Wkb Approximation ◽  
Temporal Parts ◽  
Klein Gordon ◽  
Current Energy ◽  
Particle Current

As a continuation of solving the equations governing the perturbation of the Friedmann-Lemaitre-Robertson- Walker (FLRW) space-time in Newman-Penrose formalism, the behaviour of the massive Klein-Gordon (KG) field coupled to the FLRW has been investigated. The Equation of Motion has been written and solved separately for radial and temporal parts. The former solution has come to be in terms of the Gegenbauer polynomials and spherical harmonics and the latter being in the WKB approximation. The particle current, energy momentum tensor and potential have also been obtained.

scholarly journals INTRINSIC AMBIGUITY IN SECOND-ORDER VISCOSITY PARAMETERS IN RELATIVISTIC HYDRODYNAMICS

2012 ◽  
Vol 27 (22) ◽  
pp. 1250125 ◽  
Author(s):  
YU NAKAYAMA
Keyword(s):  
Minkowski Space ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Second Order ◽  
Relativistic Hydrodynamics ◽  
Conformal Invariant ◽  
Scale Invariant ◽  
Minkowski Space Time

We show that relativistic hydrodynamics in Minkowski space–time has intrinsic ambiguity in second-order viscosity parameters in the Landau–Lifshitz frame. This stems from the possibility of improvements of energy–momentum tensor. There exist at least two viscosity parameters which can be removed by using this ambiguity in scale invariant hydrodynamics in (1+3) dimension, and seemingly nonconformal hydrodynamic theories can be hiddenly conformal invariant.

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