Quantum electrodynamics without the principle of stability of the vacuum state
A formulation of quantum mechanics is proposed in which the condition that the vacuum state must be stable is not used. A detailed examination is made of the simplest model, the electron-positron field interacting with a given external field. It is shown that in the case of a system with an unstable vacuum the particle propagators and the quantum transition amplitudes that appear in the proposed theory are quite different from those in the traditional scheme. No vacuum loops occur. The integral equations for the propagators are of more complicated structure than the usual Schwinger-Dyson equations; this is so because they take into account the influence on the entire system of pairs of particles produced by the action of the external field. When the condition that the vacuum be stable is satisfied, the usual results are obtained. A difference in the propagators and transition amplitudes arises even in the first order of perturbation theory in terms of an external field which produces pairs. One of the main peculiarities of systems with unstable vacuum states is that invariance under time displacement is violated for the matrix element <0vertical-barPsi (x) a/sup +//sub n/vertical-bar0>, where Psi (x) and a/sup +//sub n/ are the field operators and the operator for creation of an electron at t..-->..-infinity in the Heisenberg picture and vertical-bar0> is the vacuum ket vector. The generating function for particle propagators is constructed, and a representation of the electron propagator in terms of the inverse operator is derived.
- Research Organization:
- Institute of Semiconductors, Academy of Sciences of the Ukrainian SSR
- OSTI ID:
- 5747197
- Journal Information:
- Sov. J. Nucl. Phys. (Engl. Transl.); (United States), Vol. 29:4
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM ELECTRODYNAMICS
ELECTRON PAIRS
PROPAGATOR
TRANSITION AMPLITUDES
QUANTUM MECHANICS
VACUUM STATES
STABILITY
PERTURBATION THEORY
VACUUM POLARIZATION
AMPLITUDES
ELECTRODYNAMICS
FIELD THEORIES
MECHANICS
QUANTUM FIELD THEORY
645400* - High Energy Physics- Field Theory
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