scholarly journals Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation

2012 ◽  
Author(s):  
Robert Oeckl
Keyword(s):  
Field Theory ◽  
General Boundary ◽  
Linear Field ◽  
General Boundary Formulation

CONFORMALLY COVARIANT COUPLED NON-LINEAR FIELD THEORY ON THE HYPERCONE: VACUUM SOLUTIONS AND QUANTIZATION OF NORMAL MODES

1988 ◽  
Vol 03 (02) ◽  
pp. 161-165
Author(s):  
T. AÇIKTEPE ◽  
K.G. AKDENIZ ◽  
A.O. BARUT ◽  
J. KALAYCI
Keyword(s):  
Field Theory ◽  
Normal Modes ◽  
Scalar Fields ◽  
Particle Spectrum ◽  
Geometric Meaning ◽  
Model Type ◽  
Quantized Fields ◽  
Non Linear ◽  
Vacuum Solutions ◽  
Linear Field

For the conformally covariant coupled non-linear spinor-scalar fields of the σ -model type we show that the non-trivial vacuum instanton solutions have a geometric meaning as constant spinors on the five-dimensional hypercone. The quantized fields around these solutions correspond to the normal modes of the hypercone. A connection is thus established between field theory, particle spectrum of the fields and quantized excitations of a geometry (the hypercone).

A non-linear field theory

1961 ◽  
Vol 260 (1300) ◽  
pp. 127-138 ◽  
Keyword(s):  
Field Theory ◽  
Finite Energy ◽  
Unified Field Theory ◽  
Unified Field ◽  
Meson Theory ◽  
Static Solutions ◽  
Derivative Type ◽  
Type Coupling ◽  
Conserved Current ◽  
Linear Field

A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy,characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hyper-charge. The postulates include one constant of the dimensions of length, and another that is conjectured necessarily to have the value ђc , or perhaps ½ ђc , in the quantized theory.

scholarly journals Multisymplectic effective general boundary field theory

2014 ◽  
Vol 31 (9) ◽  
pp. 095013 ◽  
Author(s):  
Mona Arjang ◽  
José A Zapata
Keyword(s):  
Field Theory ◽  
General Boundary ◽  
Boundary Field

scholarly journals GENERALIZED SCHRÖDINGER EQUATION IN EUCLIDEAN FIELD THEORY

2004 ◽  
Vol 19 (24) ◽  
pp. 4037-4068 ◽  
Author(s):  
FLORIAN CONRADY ◽  
CARLO ROVELLI
Keyword(s):  
Field Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Boundary Surface ◽  
General Boundary ◽  
Classical Counterpart ◽  
Arbitrary Space ◽  
Euclidean Field Theory ◽  
Evolution Kernel ◽  
Free Scalar

We investigate the idea of a "general boundary" formulation of quantum field theory in the context of the Euclidean free scalar field. We propose a precise definition for an evolution kernel that propagates the field through arbitrary space–time regions. We show that this kernel satisfies an evolution equation which governs its dependence on deformations of the boundary surface and generalizes the ordinary (Euclidean) Schrödinger equation. We also derive the classical counterpart of this equation, which is a Hamilton–Jacobi equation for general boundary surfaces.

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