't Hooft's quantum determinism: path integral viewpoint

Blasone, Massimo; Jizba, Petr; Kleinert, H.

doi:10.1590/s0103-97332005000300022

Cited by 15 publications

(18 citation statements)

References 43 publications

(51 reference statements)

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“…The latter would render the to-be-quantum field theory unstable and are eliminated by a constraint on the physical states, based on the supersymmetry of the classical system. This is analogous to the "loss of information" condition in 't Hooft's and subsequent work [4,8,9]. We hope that the study of interacting fields will lead to better understand the dynamical origin of such a constraint.…”

Section: Introductionmentioning

confidence: 68%

Deterministic models of quantum fields

Elze

2006

J. Phys.: Conf. Ser.

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Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -In particular, a local quantum field theory is presented which is a supersymmetric classical model [1]. The Hilbert space approach of Koopman and von Neumann is used to study the classical evolution of an ensemble of such systems. Its Liouville operator is decomposed into two contributions, with positive and negative spectrum, respectively. The unstable negative part is eliminated by a constraint on physical states, which is invariant under the Hamiltonian flow. Thus, choosing suitable variables, the classical Liouville equation becomes a functional Schrödinger equation of a genuine quantum field theory. -We briefly mention an U(1) gauge theory with "varying alpha" or dilaton coupling where a corresponding quantized theory emerges in the phase space approach [2]. It is energy-parity symmetric and, therefore, a prototype of a model in which the cosmological constant is protected by a symmetry.

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Section: Introductionmentioning

confidence: 68%

Deterministic models of quantum fields

Elze

2006

J. Phys.: Conf. Ser.

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“…Appropriate rescalings by powers of l, m, , and c of the various quantities have to be incorporated, in order to give the equations their one-dimensional form, where Newton's constant G is a dimensionless parameter. If there is a nonzero potential V (φ) in our Hamiltonian, this extends the Schrödinger equation in (35) by an additional potential term. Explicitly, keeping units such that = c = 1 and considering the Hamiltonian of (9) with V (φ) ≡ 0, the following substitutions have to be performed, in order to arrive at the stationary limit of (35):…”

Section: Stationary States and The Schrödinger-newton Equationsmentioning

confidence: 89%

“…Part of the motivation for the present work comes from recent considerations of the possibility of a deterministic foundation of quantum mechanics, as it has already been verified in a number of models [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. While general principles and physical mechanisms ruling the construction of a deterministic classical model underlying a given quantum field theory are hard to come by, cf.…”

Section: Introductionmentioning

confidence: 99%

A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

Elze

2007

Int J Theor Phys

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A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schrödinger picture of a given field theory. While, for simplicity, we study the example of a U (1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0 + 1)-dimensional limit, similar to recently studied Schrödinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. A probabilistic interpretation (Born's rule) holds, provided the underlying model is scale free.

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“…When we attempt to regard quantum mechanics as a deterministic system, we have to face the problem of the positivity of the Hamiltonian, as was concluded earlier in Refs [3] [5] [6]. There, also, the suspicion was raised that information loss is essential for the resolution of this problem.…”

Section: Discussionmentioning

confidence: 99%

What is quantum mechanics?

Hooft

2007

AIP Conference Proceedings

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Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation J. Chem. Phys. 137, 22A535 (2012) The spectral shift function and Levinson's theorem for quantum star graphs J. Math. Phys. 53, 082110 (2012) Explicit formulas for noncommutative deformations of PN and HN J. Math. Phys. 53, 073502 (2012) Coherent averaging in the frequency domain AbstractWe discuss the arguments for suspecting that there exists a classical, i.e. deterministic theory underlying quantum mechanics. A difficulty is that an explanation must be found of the fact that the Hamiltonian, which is denned to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes.The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.An example of a deterministic dissipative model producing exact quantum mechanics is provided for the case of a finite-dimensional vector space. These lecture notes have been produced partly from material published earlier, and as such contain more material than what could be presented in the talk.

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't Hooft's quantum determinism: path integral viewpoint

Cited by 15 publications

References 43 publications

Deterministic models of quantum fields

Deterministic models of quantum fields

A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

What is quantum mechanics?

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