Three-phase model of a chiral quark bag

Sveshnikov, K. A.; Silaev, P. K.

doi:10.1007/bf02557171

Cited by 7 publications

(21 citation statements)

References 28 publications

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“…On the other hand, we have a well-justified counterargument to this objection, which is that when performing any consistent renormalization procedure, initial divergent expression (11) for the vacuum energy must be necessarily replaced with a convergent expression. From this standpoint, regularization methods (2) and (22) are equivalent because they both ensure the reconstruction of initial expression (1) at α → 0 and the vanishing of the vacuum energy and its first derivative at M = ∞; there is hence no physically justified reason favoring either of these regularizations.…”

Section: Results Of Calculating the Casimir Energy For A Scalar Fieldmentioning

confidence: 94%

“…We note that in contrast to relation (11) for second derivatives, it is impossible to establish a relation between ∂ L E Cas explicitly. This is because segregating a regular part from ∂ L E (r)…”

Section: Massive One-dimensional Scalar Fieldmentioning

confidence: 92%

“…We can then repeat the chain of reasoning in the preceding section, using which we pass from the quantity E (r) Cas , which is divergent after removing the regularization, to the finite vacuum field energy E (r) Cas . In particular, we have the analogue of relation (11), which, being written in terms of dimensionless spectrum (17) and the new scaling variable M instead of L, becomes…”

Section: Subtraction-free Methods For Calculating the Casimir Energy Imentioning

confidence: 99%

“…As the result, the final answer contains the ambiguity related to d. Normalizing the final answer at L → ∞ becomes impossible here because the ambiguity has the form const /L, i.e., the ambiguity enters precisely the constant we must find. A concrete example of this type was considered in detail in [11] in the context of chiral bag models in the dimension 1 + 1.…”

Section: Introductionmentioning

confidence: 99%

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Subtraction-free renormalization of the quantum-field vacuum energy in the presence of nontrivial boundary conditions

2005

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We propose a subtraction-free method for calculating the quantum-field vacuum energy in the presence of nontrivial boundary conditions and logarithmically divergent terms caused by them. The method can also be used in the case where the energy levels of a system are known only numerically. Moreover, its use requires neither knowledge of the analytic form of equations for certain levels nor a detailed analysis of their asymptotic behavior.

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Section: Results Of Calculating the Casimir Energy For A Scalar Fieldmentioning

confidence: 94%

Section: Massive One-dimensional Scalar Fieldmentioning

confidence: 92%

Section: Subtraction-free Methods For Calculating the Casimir Energy Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Subtraction-free renormalization of the quantum-field vacuum energy in the presence of nontrivial boundary conditions

2005

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“…(1.7) are in direct relation to the models of chiral quark bags in the (1+1)-dimensional case [13]. In representation (3.3), for the upper and lower components u and v of the spinor (3.4) we obtain the expressions…”

Section: Quasi-exact Solution For Fermion Bound Statesmentioning

confidence: 97%

Quasi-exact solution of the problem of relativistic bound states in the (1+1)-dimensional case

Sveshnikov

Silaev

2006

Theor Math Phys

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We investigate the problem of bound states for bosons and fermions in the framework of the relativistic configurational representation with the kinetic part of the Hamiltonian containing purely imaginary finite shift operators e ±i d/dx instead of differential operators. For local (quasi)potentials of the type of a rectangular potential well in the (1+1)-dimensional case, we elaborate effective methods for solving the problem analytically that allow finding the spectrum and investigating the properties of wave functions in a wide parameter range. We show that the properties of these relativistic bound states differ essentially from those of the corresponding solutions of the Schrödinger and Dirac equations in a static external potential of the same form in a number of fundamental aspects both at the level of wave functions and of the energy spectrum structure. In particular, competition between and the potential parameters arises, as a result of which these distinctions are retained at low-lying levels in a sufficiently deep potential well for 1 and the boson and fermion energy spectra become identical.

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Calculation of ground state energy for confined fermion fields

Cherednikov

2001

Physics Letters B

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A method for renormalization of the Casimir energy of confined fermion fields in (1 + 1)D is proposed. It is based on the extraction of singularities which appear as poles at the point of physical value of the regularization parameter, and subsequent compensation of them by means of redefinition of the "bare" constants. A finite ground state energy of the two-phase hybrid fermion bag model with chiral boson-fermion interaction is calculated as the function of the bag's size.

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Three-phase model of a chiral quark bag

Cited by 7 publications

References 28 publications

Subtraction-free renormalization of the quantum-field vacuum energy in the presence of nontrivial boundary conditions

Subtraction-free renormalization of the quantum-field vacuum energy in the presence of nontrivial boundary conditions

Quasi-exact solution of the problem of relativistic bound states in the (1+1)-dimensional case

Calculation of ground state energy for confined fermion fields

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