Renormalizability of the functional schrödinger picture in Robertson-Walker space-time

Éboli, O. J. P.; Pi, So‐Young; Samiullah, M.

doi:10.1016/0003-4916(89)90354-0

Cited by 30 publications

(46 citation statements)

References 15 publications

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“…[28,34] In the case of isoentropic time evolutions, these variational techniques have allowed detailed discussions of a wide range of physical phenomena, from statistical physics to inflationary cosmology. [34,35] Their application to the study of quantum dynamical semigroups within the framework presented in the previous sections will surely provide new insights on the behaviour of open quantum systems.…”

Section: Discussionmentioning

confidence: 99%

Damped harmonic oscillators in the holomorphic representation

Benatti¹,

Floreanini²

2000

J. Phys. A: Math. Gen.

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Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the holomorphic representation. Bosonic and fermionic degrees of freedom are then put together to form a supersymmetric oscillator; the conditions that assure supersymmetry invariance of the corresponding dynamical equations are explicitly derived.

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Section: Discussionmentioning

confidence: 99%

Damped harmonic oscillators in the holomorphic representation

Benatti¹,

Floreanini²

2000

J. Phys. A: Math. Gen.

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“…In the soliton quantization language [1,2] Ψ specifies whether the quantum soliton is in the ground or excited state. For the Gaussian approach [14,15,16,17], Ψ specifies the form of the Gaussian functional, while for QFT in the strong external classical field [6,7] Ψ is a state of a quantum field in the classical background.…”

Section: Discussionmentioning

confidence: 99%

“…The one-loop approximation [8,9,10,11], the time-dependent Hartree-Fock approximation [8,9,12,13] and the Gaussian approximation developed in [14,15,16,17] may be also viewed as examples of applications of semiclassical conceptions.…”

Section: Introductionmentioning

confidence: 99%

“…To illustrate the formal semiclassical ansatz for the state vector, use the functional Schrodinger representation (see, for example, [12,13,16,17]). States at fixed moment of time are represented as functionals ψ[ϕ(·)] depending on fields ϕ(x), x ∈ R d , the field operatorφ(x) is the operator of multiplication by ϕ(x), while the canonically conjugated momentumπ(x) is represented as a differentiation operator −iδ/δϕ(x).…”

Section: Introductionmentioning

confidence: 99%

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Renormalization of Poincaré transformations in Hamiltonian semiclassical field theory

Shvedov

2002

Journal of Mathematical Physics

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Semiclassical Hamiltonian field theory is investigated from the axiomatic point of view. A notion of a semiclassical state is introduced. An "elementary" semiclassical state is specified by a set of classical field configuration and quantum state in this external field. "Composed" semiclassical states viewed as formal superpositions of "elementary" states are nontrivial only if the Maslov isotropic condition is satisfied; the inner product of "composed" semiclassical states is degenerate. The mathematical proof of Poincare invariance of semiclassical field theory is obtained for "elementary" and "composed" semiclassical states. The notion of semiclassical field is introduced; its Poincare invariance is also mathematically proved.

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“…Examples of application of semiclassical conceptions are soliton quantization [3,4,5,20], quantum field theory in a strong external background [7,8], one-loop [9,10,11,12], time-dependent Hartree-Fock [13,14] and Gaussian approximations [15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Semiclassical Symmetries

Shvedov¹

2002

Annals of Physics

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Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are considered. An infinitesimal analog of group relation is written. Sufficient conditions for reconstructing semiclassical group transformations (integrability of representation of Lie algebra) are discussed. The obtained results may be used for mathematical proof of Poincare invariance of semiclasical Hamiltonian field theory and for investigation of quantum anomalies.

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Renormalizability of the functional schrödinger picture in Robertson-Walker space-time

Cited by 30 publications

References 15 publications

Damped harmonic oscillators in the holomorphic representation

Damped harmonic oscillators in the holomorphic representation

Renormalization of Poincaré transformations in Hamiltonian semiclassical field theory

Semiclassical Symmetries

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