Quantum theory in curved spacetime using the Wigner function

Antonsen, Frank

doi:10.1103/physrevd.56.920

Cited by 24 publications

(32 citation statements)

References 25 publications

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“…This is something which has not been done yet in the literature. And at the same time this is the natural extension of the deformation quantization of classical fields developed in [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Deformation quantization of bosonic strings

García‐Compeán¹,

Plebański²,

Przanowski³

et al. 2000

J. Phys. A: Math. Gen.

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Deformation quantization of bosonic strings is considered. We show that the light-cone gauge is the most convenient classical description to perform the quantization of bosonic strings in the deformation quantization formalism. Similar to the field theory case, the oscillator variables greatly facilitates the analysis. The mass spectrum, propagators and the Virasoro algebra are finally described within this deformation quantization scheme.

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Section: Introductionmentioning

confidence: 99%

Deformation quantization of bosonic strings

García‐Compeán¹,

Plebański²,

Przanowski³

et al. 2000

J. Phys. A: Math. Gen.

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“…Deformation quantization of gravitational field as a constrained system has been discussed in [11,12].…”

Section: Introductionmentioning

confidence: 99%

Deformation quantization of fermi fields

et al. 2008

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Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal ⋆-product and the Wigner functional are obtained by extending the formalism proposed recently in [35] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal ⋆-product, the Wigner functional, the normal ordering operator, and finally, the Dirac propagator have been found with the use of these variables.

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“…between the two points [9,10]. While its generalization to curved spacetimes has been studied [11][12][13][14][15][16], the treatment of Ref. [16] is particularly suitable for our aim since it adopts a spatially covariant formalism based on the 3+1 decomposition of the spacetime and considers a real scalar field, which is of our interest in the present paper.…”

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confidence: 99%

Kinetic equation for Lifshitz scalar

Mukohyama

Watanabe

2019

Phys. Rev. D

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Employing the method of Wigner functions on curved spaces, we study classical kinetic (Boltzmann-like) equations of distribution functions for a real scalar field with the Lifshitz scaling. In particular, we derive the kinetic equation for z = 2 on general curved spaces and for z = 3 on spatially flat spaces under the projectability condition N = N (t), where z is the dynamical critical exponent and N is the lapse function. We then conjecture a form of the kinetic equation for a real scalar field with a general dispersion relation in general curved geometries satisfying the projectability condition, in which all the information about the nontrivial dispersion relation is included in the group velocity and which correctly reproduces the equations for the z = 2 and z = 3 cases as well as the relativistic case. The method and equations developed in the present paper are expected to be useful for developments of cosmology in the context of Hořava-Lifshitz gravity. I. INTRODUCTIONGravitational phenomena observed to the present are well described by general relativity (GR). However, at short distances quantum gravity effects become significant and GR loses its predictability. Among various approaches to quantum gravity, Hořava-Lifshitz (HL) gravity is unique in the sense that it is a local field theory of gravity which is perturbatively renormalizable at least at the power-counting level and which is free from the Ostrogradsky ghost [1]. The theory is rendered power-counting renormalizable by the scaling anisotropic in space and time (the so-called Lifshitz scaling) at high energy,and recovers the usual isotropic scaling at low energy. Here, z is a constant often called the dynamical critical exponent and b is an arbitrary constant. The renormalizability beyond the power-counting level has recently been proven in the minimal setup called the projectable theory, where the lapse function depends only on time [2, 3]. As for observational constraints on parameters, see, e.g., Refs. [4,5] for the nonprojectable theory and Sec. 3.2 of Ref.[6] for the projectable theory. Since HL gravity is a candidate for quantum gravity and thus can presumably describe gravity at very short distances, it is natural to seek its implications to the early universe cosmology [6]. In the early universe or at high energies, it is expected from theoretical consistency that not only the gravity sector but also the matter sector should exhibit the Lifshitz scaling. A field in the matter sector should then obey a dispersion relation of the form ω 2 ∼ (k 2 /a 2 ) z /M 2(z−1) in the early universe, where k is the comoving momentum, a is the scale factor of the universe, M is the (momentum) scale characterizing the Lifshitz scaling, and z is the dynamical critical exponent. The energy of each high energy particle should decay as ω ∝ 1/a z as the universe expands. As a result the energy density of a gas of Lifshitz particles should decay as ρ z ∝ 1/a z+3 [7]. In reality, we need to consider the transition from a high value of z to lower values, say, from...

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Quantum theory in curved spacetime using the Wigner function

Cited by 24 publications

References 25 publications

Deformation quantization of bosonic strings

Deformation quantization of bosonic strings

Deformation quantization of fermi fields

Kinetic equation for Lifshitz scalar

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