A necessary condition for the validity of Huygens’ principle on a curved space–time

1977 ◽  
Vol 18 (11) ◽  
pp. 2125-2128 ◽  
Author(s):  
Riccardo Goldoni
Keyword(s):  
Space Time ◽  
Necessary Condition ◽  
Curved Space ◽  
Huygens Principle

SEPARATION OF VARIABLES FOR THE DIRAC SQUARE EQUATION

1994 ◽  
Vol 03 (04) ◽  
pp. 739-746 ◽  
Author(s):  
V.G. BAGROV ◽  
V.V. OBUKHOV
Keyword(s):  
Jacobi Equation ◽  
Separation Of Variables ◽  
Complete Separation ◽  
Space Time ◽  
Riemann Space ◽  
Necessary Condition ◽  
Separation Procedure ◽  
Electromagnetic Potential ◽  
Curved Space ◽  
Hamilton Jacobi Equation

The problem of separation of variables for the Dirac square equation on a curved space-time in the presence of electromagnetic potential is considered. It is shown that the necessary condition for the separation of variables in the Dirac square equation is the complete separation of variables in the related Hamilton-Jacobi equation, i.e. the Riemann space should be Stäckel. The constructive scheme for separation procedure is presented.

An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle

1969 ◽  
Vol 65 (1) ◽  
pp. 139-155 ◽  
Author(s):  
R. G. McLenaghan
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Empty Space ◽  
Space Time ◽  
Necessary Condition ◽  
Scalar Wave ◽  
Wave Space ◽  
Huygens Principle ◽  
Necessary And Sufficient

AbstractThe validity of Huygens' principle in the sense of Hadamard's ‘minor premise’ is investigated for scalar wave equations on curved space-time. A new necessary condition for its validity in empty space-time is derived from Hadamard's necessary and sufficient condition using a covariant Taylor expansion in normal coordinates. A two component spinor calculus is then employed to show that this necessary condition implies that the plane wave space-times and Minkowski space are the only empty space-times on which the scalar wave equation satisfies Huygens' principle.

Path integrals and the solution of the Schwinger model in curved space-time

1986 ◽  
Vol 33 (8) ◽  
pp. 2262-2266 ◽  
Author(s):  
J. Barcelos-Neto ◽  
Ashok Das
Keyword(s):  
Path Integrals ◽  
Space Time ◽  
Curved Space ◽  
Schwinger Model

scholarly journals ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Njl Model ◽  
Effective Lagrangian ◽  
Special Solutions ◽  
Curvature Approximation ◽  
Symmetric Phase

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

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