Quantum Fields in Accelerated Frames

Narozhny, N. B.; Fedotov, A. M.; Karnakov, B. M.; Mur, V. D.; Belinskiǐ, V. A.

doi:10.1002/(sici)1521-3889(200005)9:3/5<199::aid-andp199>3.0.co;2-i

Cited by 13 publications

(16 citation statements)

References 17 publications

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“…Of course, 3 It is worth to remark that in this model the zero condition for the incident waves on the last ray will produce inevitably the zero boundary condition for the outgoing waves at points of the horizon in the external space (region BADH, Fig.l). One of the possibilities is to say that we have the zero boundary condition for the incident waves at the points of the last ray.…”

Section: F Smentioning

confidence: 99%

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“…Formulas (2)- (3) show that modes V2W K _ K i(t,x) indeed accomplish a representation of the translation operator T(t,x) since they are its matrix elements between the states with eigenvalues K and K'. From the same equations (104) and (106) one can get the following relation for these matrix elements:…”

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Quantum Fields in Black Hole Space-Time and in Accelerated Systems

Belinski¹

2007

AIP Conference Proceedings

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In articles [1][2][3][4][5][6][7] it was shown the absence of a theoretical grounds for the so-called Unruh effect and papers [8,9] showed the same about black hole evaporation phenomenon. The present paper offers a short description of the content of these works and represents a synopsis of the lectures delivered by the author at XII Brazilian School of Cosmology and Gravitation in Rio-de-Ianeiro at September 2006. For the reader interested in a general understanding of the essence of the problem the paper is complete and self-consistent. For those who would like to study the question in details would be reasonable to become familiar also with the aforementioned original works and some of the literature cited there. However, it should be stressed that there is no need to look for all papers [1-9] as they partially over-cross each other. To get complete information on our results the study of articles [4-7] and [9] would be enough. ON THE UNRUH EFFECTUnruh effect consists of the statement: in Minkowski space-time filled by some quantum field in the state of the standard Minkowski vacuum an accelerated observer perceives the environment as mixed thermal state at the temperature (we use units c = h = k^ = 1):where a is the constant observer's acceleration measured in his instantaneously co-moving reference system. This statement can not be correct due to the following reasons. Any mixed state is a statistical mixture of the pure ones but the last can be constructed only out of the one-particle states with finite energy. Because the question is of the states defined for an observer living in the right Rindler sector R (the definition of sectors see in Appendix A), the field quantization in terms and notions which belong only to this region should provide the presence of such one-particle states (people often call them the Rindler particles) in the corresponding Hilbert space. However, it is not so difficult to show (see [4], sections II and III), that they exist if and only if the field satisfies the zero boundary condition at the left edge of the R wedge, that is at the origin (t,x) = (0,0) of the Minkowski space-time. From another side it is clear that this is impossible because the Minkowski vacuum is translationally invariant and such symmetry is incompatible with zero boundary condition even at one finite point of Minkowski space-time.The foregoing means that in the conventional derivation of the Unruh effect should be some hidden insolvency. The analysis show that the problem is in non-adequate use of the so-called boost modes (see its definition in Appendix B) for the quantization of the free field in Minkowski space-time. In canonical approach the use of such modes is compulsory if one wish to find a connection between quantization in Minkowski space-time and in the region R, since the boost modes are the analytical continuation to the entire Minkowski space-time of the Fulling modes (defined in Appendix A), that is namely of those modes which form the basis for the field quantization in the R wedge [10].O...

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Quantum Fields in Black Hole Space-Time and in Accelerated Systems

Belinski¹

2007

AIP Conference Proceedings

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“…Most of the results reviewed here were obtained [9][10][11][12][13][14][15][16]29 in collaboration with our colleagues Vladimir Belinski, Vadim Mur, Evgeny Gelfer and Boris Karnakov. This work was supported by the Russian Foundation for Basic Research (grant 16-02-00963) and the Russian Federation President program for support of the leading research schools.…”

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confidence: 99%

“…Though our presentation is simple and visual, it is rather condensed. Further details can be found in our previous publications [9][10][11][12][13][14][15][16] . For the sake of simplicity, we almost everywhere assume D = 1 + 1 and use the units = c = 1.…”

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Scalar and fermion representations of the Lorentz group in Minkowski plane, QFT correlators, pair creation in electric field and the Unruh effect

Fedotov

Narozhny

2017

The Fourteenth Marcel Grossmann Meeting

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Boost modes Ψκ (x) are eigenfunctions of the Lorentz transformations generator in twodimensional (2D) Minkowski space (MS). We demonstrate and discuss deep interrelation between the boost modes and the field correlators, also known as Wightman functions. In the case of a massive scalar field, the boost modes, as functions of the spectral parameter κ, contain the Dirac delta-function singularity δ(κ) at the light cone. The zero boost mode coincides up to a constant factor with the Wightman function. The light cone singularity of boost modes for a fermion field is stronger. For this case, they contain the Gelfand δ-function of complex argument δ(κ ± i/2), while the Wightman function components coincide with analytical continuation of the boost modes set towards the spectral values κ = ∓i/2. We argue that due to the discovered properties of the boost modes the so-called Unruh modes, which are at the core of the Unruh effect derivation, do not constitute a complete set in MS and thus cannot be used for quantization of neither scalar, nor fermion field. Finally, we discuss boost modes for the case of the constant electric background and rederive the well-known result for spontaneous pair creation rate. Solution of this problem in the boost modes representation reveals distinctions between the Unruh problem and the effect of pair creation by an electric field in vacuum.

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Boost modes for a massive fermion field and the Unruh problem

et al. 2015

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We have shown that Wightman function of a free quantum field generates any complete set of solutions of relativistic wave equations. Using this approach we have constructed the complete set of solutions to 2d Dirac equation consisting of eigenfunctions of the generator of Lorentz rotations (boost operator). It is shown that at the surface of the light cone the boost modes for a fermion field contain δ-function of a complex argument. Due to the presence of such singularity exclusion even of a single mode with an arbitrary value of the boost quantum number makes the set of boost modes incomplete.

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Quantum Fields in Accelerated Frames

Abstract: We have considered quantization of free massive scalar field in Minkowski and Rindler spacetimes both in canonical and algebraic approaches. It is shown that general principles of quantum field theory do not give any grounds for existence of the Unruh effect.

Cited by 13 publications

References 17 publications

Quantum Fields in Black Hole Space-Time and in Accelerated Systems

Quantum Fields in Black Hole Space-Time and in Accelerated Systems

Scalar and fermion representations of the Lorentz group in Minkowski plane, QFT correlators, pair creation in electric field and the Unruh effect

Boost modes for a massive fermion field and the Unruh problem

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