Quantum Field Theory and Parastatistics

Ohnuki, Yoshio; Kamefuchi, S.

doi:10.1007/978-3-642-68622-1

Cited by 376 publications

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“…In the transverse gauge, in order to have [M i− , M j− ] = 0, the space-time critical dimension D is calculated with the only use of the trilinear relations (8). Like in Ardalan and Mansouri work [5], D is again given as function of the paraquantization order through the relation D = 2 + 8 Q .…”

Section: Resultsmentioning

confidence: 99%

“…These authors paraquantize the excitation modes of the string and impose to the center of mass variables to satisfy the ordinary quantum commutation relations. This is done by the choice of a specific direction in the paraspace of the Green components [6], [7], [8], which requires relative paracommutation relations between the center of mass variables and the excitation modes of the string. In order that the theory is Poincaré invariant, the space-time dimension D and the order of the paraquantization Q are related by the relation D = 2+ 8 Q .…”

Section: Introductionmentioning

confidence: 99%

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Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

Belaloui

Bennacer

2004

Czechoslovak Journal of Physics

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In this paper, we paraquantize the spinning string theory in the Neuveu-Shwarz model . Both the center of mass variables and the excitation modes of the string verify paracommutation relations. Except the [p µ , p ν ] commutator, the two other commutators of Poincaré algebra are satisfied. With the sole use of trilinear relations we find existence possibilities of spinning strings at space-time dimensions other than D = 10.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

Belaloui

Bennacer

2004

Czechoslovak Journal of Physics

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“…By construction H P ⊆ H G and G P ⊆ G. Moreover, the intersection of H P and any G-invariant subspace of H G , if non-trivial, consists of only a single state vector. (For a proof of this fact, see Ohnuki and Kamefuchi [1982], p.117-118.) Thus any G P -invariant sector of the parafield system will correspond to some G-invariant sector in the enlarged Green field system, and the invariants of the latter can be used to non-degenerately label the former.…”

Section: The Argument Of Drühl Haag and Robertsmentioning

confidence: 95%

The Conventionality of Parastatistics

Baker¹,

Halvorson²,

Swanson³

2015

The British Journal for the Philosophy of Science

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Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles make perfect physical sense, so why don't we see them in nature? We consider one potential answer: every paraparticle theory is physically equivalent to some theory of bosons or fermions, making the absence of paraparticles in our theories a matter of convention rather than a mysterious empirical discovery.We argue that this equivalence thesis holds in all physically admissible quantum field theories falling under the domain of the rigorous Doplicher-Haag-Roberts approach to superselection rules. Inadmissible parastatistical theories are ruled out by a localityinspired principle we call Charge Recombination.

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“…Moreover, note that in the case of positively definite metric and when R ++ = R −− = 0, the equations (2.8) coincide with the basic commutations relations for the single-mode parafermion [16]. Now let us consider the following modification of the three-dimensional matrix model [17] …”

Section: Matrix Modelsmentioning

confidence: 99%

Dolan–Grady relations and noncommutative quasi-exactly solvable systems

Klishevich

Plyushchay

2003

J. Phys. A: Math. Gen.

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We investigate a U (1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2, R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems. *

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Quantum Field Theory and Parastatistics

Cited by 376 publications

References 0 publications

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

The Conventionality of Parastatistics

Dolan–Grady relations and noncommutative quasi-exactly solvable systems

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