An Introduction to Field Quantization

Takahashi, Yasushi; Hammer, C. L.

doi:10.1119/1.1976398

Cited by 50 publications

(60 citation statements)

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“…ref. [ 20] ) one gets the following formulae for the K-extension of the scalar field Green functions: It is easy to see that the p 0 -integration in ( 4. 7) is damped exponentially.…”

Section: K-deformed Free Field Theorymentioning

confidence: 99%

“…We would like to add the following: (i) Using the know techniques for higher order lagrangian theories [20,21] We see from ( 5.8) that the K-deformation of the Dirac operator is given by the replacement of the time derivative by a q-deformed time derivative, with Kdependent deformation parameter ln q= i/2K. (iii) An interesting question is to reconcile the nontrivial coproducts with the form of the vertex operators describing interaction.…”

Section: K-deformed Free Field Theorymentioning

confidence: 99%

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New quantum Poincaré algebra and κ-deformed field theory

1992

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We derive a new real quantum Poincare algebra with standard real structure, obtained by contraction ofUq(0(3, 2)) (q real) , which is a standard real Hopf algebra, depending on a dimension-full parameter K instead of q. For our real quantum Poincare algebra both Casimirs are given. The free scalar K-deformed quantum field theory is considered. it appears that the K-parameter introduced nonlocal q-time derivatives with In q-1 /K.

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“…ref. [ 20] ) one gets the following formulae for the K-extension of the scalar field Green functions: It is easy to see that the p 0 -integration in ( 4. 7) is damped exponentially.…”

Section: K-deformed Free Field Theorymentioning

confidence: 99%

Section: K-deformed Free Field Theorymentioning

confidence: 99%

New quantum Poincaré algebra and κ-deformed field theory

1992

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“…Substituting the results of <ls<v>>, <.511s<v>>, <'Jls<v>> and <L> obtained in the previous section into Eqs. (3)~(5), we can calculate the scalar and vector momentum distributions, (16) and (17), of the constituent-quarks in relativistic nuclear matter. It is assumed that interacting relativistic nuclear matter is described by the relativistic Hartree-Fock model.…”

Section: Resultsmentioning

confidence: 99%

“…Each wave function of these octet members is expressed by the third-rank Bargmann-Wigner wave function BraPJr: 17 ) ms b-(Bs )b . : (14) where Cis the charge conjugation operator, KP.=-(EK, K) denotes the four-momentum of the baryon and M is its mass.…”

Section: Outline Of Formulationmentioning

confidence: 99%

Quark Momentum Distributions in Relativistic Nuclear Matter

Miyazaki

1994

Progress of Theoretical Physics

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We develop the relativistic extension of the study of the (constituent-)quark momentum distribution in nuclear matter by Arifuzzaman, Hasan and Hoodbhoy. This is performed by employing the relativistic SU(6) model for nucleons and the relativistic Hartree(-Fock) model for nuclear matter. However, the Gaussian function is introduced by hand to describe the quark momentum distribution in a nucleon. Our main interest is in the effect of the relativistic effective mass of nucleons, which is reduced to be smaller than the free value by the mean scalar-meson field, on the quark exchange contribution. We calculate the scalar and vector quark momentum distributions in the interacting relativistic nuclear matter with M*=0.515 M. The differences between the results of the nonrelativistic and relativistic calculations of the total distributions are small. However, as for the quark exchange contributions the differences between them are significant. In other words, the relativistic effect enhances the quark exchange contribution. We therefore• calculate the ratio which is called the EMC ratio. The effect of the relativistic mean-field lowers the value of the nonrelativistic calculation considerably. It is found that the relativistic result agrees with the nonrelativistic one with effectively swollen nucleons.

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“…It is connected with the fact that the second order Kemmer equation [27] lacks a back-transformation which would allow one to obtain solutions of the first order DKP equation from solutions of the second order equation, as is the case in Dirac's theory. The reason of the latter is that the Klein-Gordon-Fock divisor [78,79] in the spin-1 case 2…”

Section: Jhep07(2020)094 2 Third-order Wave Operatormentioning

confidence: 99%

Path integral representation for inverse third order wave operator within the Duffin-Kemmer-Petiau formalism. Part I

Markov

Markova

Bondarenko

2020

J. High Energ. Phys.

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Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism with a deformation, an approach to the construction of the path integral representation in parasuperspace for the Green's function of a spin-1 massive particle in external Maxwell's field is developed. For this purpose a connection between the deformed DKP-algebra and an extended system of the parafermion trilinear commutation relations for the creation and annihilation operators a ± k and for an additional operator a 0 obeying para-Fermi statistics of order 2 based on the Lie algebra so(2M + 2) is established. The representation for the operator a 0 in terms of generators of the orthogonal group SO(2M) correctly reproducing action of this operator on the state vectors of Fock space is obtained. An appropriate system of the parafermion coherent states as functions of para-Grassmann numbers is introduced. The procedure of the construction of finite-multiplicity approximation for determination of the path integral in the relevant phase space is defined through insertion in the kernel of the evolution operator with respect to para-supertime of resolutions of the identity. In the basis of parafermion coherent states a matrix element of the contribution linear in covariant derivativeD µ to the time-dependent Hamilton operatorĤ(τ), is calculated in an explicit form. For this purpose the matrix elements of the operators a 0 , a 2 0 , the commutators [a 0 , a ± n ], [a 2 0 , a ± n ], and the productÂ[a 0 , a ± n ] withÂ ≡ exp −i 2π 3 a 0 , were preliminary defined.

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An Introduction to Field Quantization

Cited by 50 publications

References 0 publications

New quantum Poincaré algebra and κ-deformed field theory

New quantum Poincaré algebra and κ-deformed field theory

Quark Momentum Distributions in Relativistic Nuclear Matter

Path integral representation for inverse third order wave operator within the Duffin-Kemmer-Petiau formalism. Part I

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