scholarly journals CANONICAL QUANTIZATION OF NONLOCAL FIELD EQUATIONS

1996 ◽  
Vol 11 (12) ◽  
pp. 2111-2126 ◽  
Author(s):  
D.G. BARCI ◽  
L.E. OXMAN ◽  
M. ROCCA
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Canonical Quantization ◽  
Field Operator ◽  
Kinetic Term ◽  
Field Equations ◽  
Commutator Algebra ◽  
Reducible Representation ◽  
Nonlocal Equations ◽  
Nonlocal Field

We consistently quantize a class of relativistic nonlocal field equations characterized by a nonlocal kinetic term in the Lagrangian. We solve the classical nonlocal equations of motion for a scalar field and evaluate the on-shell Hamiltonian. The quantization is realized by imposing Heisenberg’s equation, which leads to the commutator algebra obeyed by the Fourier components of the field. We show that the field operator carries, in general, a reducible representation of the Poincaré group. We also consider the Gupta-Bleuler quantization of a nonlocal gauge theory and analyze the propagators and the physical modes of the gauge field.

U(2) GAUGE THEORY ON NONCOMMUTATIVE GEOMETRY

2009 ◽  
Vol 24 (15) ◽  
pp. 2889-2897
Author(s):  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Local Symmetry ◽  
Noncommutative Space ◽  
Gauge Fields ◽  
Zeroth Order ◽  
Field Equations ◽  
Relativistic Analog ◽  
Analog Form ◽  
General Relativistic

We develop a model of gauge theory with U (2) as local symmetry group over a noncommutative space-time. The integral of the action is written considering a gauge field coupled with a Higgs multiplet. The gauge fields are calculated up to the second order in the noncommutativity parameter using the equations of motion and Seiberg-Witten map. The solutions are determined order by order supposing that in zeroth-order they have a general relativistic analog form. The Wu-Yang ansatz for the gauge fields is used to solve the field equations. Some comments on the quantization of the electrical and magnetical charges are also given, with a comparison between commutative and noncommutative cases.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

scholarly journals Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

Feldtheoretische Konstruktion der Jordan—Brans—Dicke-Theorie / Fieldtheoretic Construction of the Jordan-Brans-Dicke-Theory

1971 ◽  
Vol 26 (4) ◽  
pp. 599-622
Author(s):  
H. von Grünberg
Keyword(s):  
Gauge Group ◽  
Tensor Field ◽  
Mathematical Proof ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Flat Space ◽  
Momentum Tensor ◽  
Field Equations ◽  
Tensor Theory ◽  
Generally Covariant

Abstract In the framework of Lorentz invariant theories of gravitation the fieldtheoretic approach of the generally covariant Jordan-Brans-Dicke-theory is investigated.It is shown that a slight restriction of the gauge group of Einstein's linear tensor theory leads to the linearized Jordan-Brans-Dicke-theory. The problem of the inconsistency of the field equations and the equations of motion is solved by introducing the Landau-Lifschitz energy momentum tensor of the gravitational field as an additional source term into the field equations. The second order of the theory together with the corresponding gauge group are calculated explicitly. By means of the structure of the gauge group of the tensor field it is possible to identify the successive orders of the scalar-tensor theory as an expansion of the Jordan-Brans-Dicke-theory in flat space-time. The question of the uniqueness of the procedure is answered by showing that the structure of the gauge group of the tensor field is predetermined by the linear equations of motion. The mathematical proof of this fact confirms formally the meaning of the equations of motion for the geometry of space.

Global dynamical time for binary point-like particle systems

2020 ◽  
Vol 17 (09) ◽  
pp. 2050131
Author(s):  
Osvaldo M. Moreschi
Keyword(s):  
Equations Of Motion ◽  
Minkowski Spacetime ◽  
Particle Systems ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Retarded Time ◽  
Dynamical Time ◽  
The Difference ◽  
Multiple Particle ◽  
Equations Of Motions

A geometrical construction for a global dynamical time for binary point-like particle systems, modeled by relativistic equations of motions, is presented. Thus, we provide a convenient tool for the calculation of the dynamics of recent models for the dynamics of black holes that use individual proper times. The construction is naturally based on the local Lorentzian geometry of the spacetime considered. Although in this presentation we are dealing with the Minkowskian spacetime, the construction is useful for gravitational models that have as a seed Minkowski spacetime. We present the discussion for a binary system, but the construction is obviously generalizable to multiple particle systems. The calculations are organized in terms of the order of the corresponding relativistic forces. In particular, we improve on the Darwin and Landau–Lifshitz approaches, for the case of electromagnetic systems. We discuss the possibility of a Lagrangian treatment of the retarded effects, depending on the nature of the relativistic forces. The higher-order contractions are based on a Runge–Kutta type procedure, which is used to calculate the quantities at the required retarded time, by increasing evaluations of the forces at intermediate times. We emphasize the difference between approximation orders in field equations and approximation orders in retarded effects in the equations of motion. We show this difference by applying our construction to the binary electromagnetic case.

scholarly journals The spinless relativistic Hellmann problem

2019 ◽  
Vol 34 (05) ◽  
pp. 1950028
Author(s):  
Wolfgang Lucha ◽  
Franz F. Schöberl
Keyword(s):  
Coulomb Potential ◽  
Bound States ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Kinetic Term ◽  
Discrete Eigenvalue ◽  
Hellmann Potential ◽  
Relativistic Equations

We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as superpositions of an attractive Coulomb potential and an either attractive or repulsive Yukawa potential and, hence, generalizations of the Hellmann potential employed in several areas of science. These insights should provide useful guidelines to all attempts of finding appropriate descriptions of bound states by (semi-)relativistic equations of motion.

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