Research Article
Strongly Coupled Fermions in Odd Dimensions and the Running Cut-off Λd
Evangelos Georgiou Filothodoros
Issue:
Volume 13, Issue 1, February 2024
Pages:
1-11
Received:
30 October 2023
Accepted:
23 November 2023
Published:
11 January 2024
Abstract: One may observe that the fermionic U(N) Gross-Neveu model at imaginary chemical potential and finite temperature for odd d dimensions, in the strong coupling regime, by using the gap (saddle point) equation for the fermion condensate of the model. This equation describes the phase transitions from weak to strong coupling regime. It is pointed out that the higher odd dimensional gap equations are linear combinations of the lower dimensional equations in a way that as the dimension of the model increases the lower dimensions are weaker coupled but still in the strong coupling regime. Interestingly, at a specific value of the chemical potential, exactly in the middle of the thermal windows that separate the fermionic from the bosonic (condensed) state of the fermions, it is found that the mass of the fermion condensate for d = 3, 5, 7, 9. An anomaly occurs at the 5 dimensional theory where it is stronger coupled against other theories in higher dimensions and lower energy. The main idea of this work is that the cut-off Λ regulator for the UV divergent parts of the fermion mass saddle point equation, plays the role of a physical parameter that makes the separation of the odd dimensional fermionic theories according to how deep they are in the strong coupling regime. This idea is based on the identity of the asymptotic freedom of the Gross-Neveu model as a toy model for QCD.
Abstract: One may observe that the fermionic U(N) Gross-Neveu model at imaginary chemical potential and finite temperature for odd d dimensions, in the strong coupling regime, by using the gap (saddle point) equation for the fermion condensate of the model. This equation describes the phase transitions from weak to strong coupling regime. It is pointed out t...
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Communication
Analytical Study of the Behavioral Trend of Klein-Gordon Equation in Different Potentials
Emmanuel Ifeanyi Ugwu*,
Idu Hyacenth Kevin
Issue:
Volume 13, Issue 1, February 2024
Pages:
12-16
Received:
19 January 2024
Accepted:
29 January 2024
Published:
28 February 2024
Abstract: In this work, we present the analysis of behavioral trend of Klein-Gordon Equation involving potential as regards when it comes to the study of particle, it has been observed that in every case of handling of KGE with potential of any type, it is made clear here that the equation has to first off all be transformed into a particular standard differential equation with a well-known solution which appears in form of implicitly defined transcendental equation. The equation on the other hand is to be solved analytically since the exact solution is not easily attainable without the use of mathematical tool especially when it comes to the consideration of the energy eigenvalue and the corresponding wave function because the solution is also always accompanied with a normalization constant often coupled with a condition that requires an arbitrarily chosen quantum number that come up when (l=0) and so on. In general, the analysis reveals the fact that the of trend of KGE involving potential gives a good understanding in the study of inter-molecular structure, diatomic crystals, and such case that involves inter-atomic interaction which is gives very nice idea in the study of bound state in atom.
Abstract: In this work, we present the analysis of behavioral trend of Klein-Gordon Equation involving potential as regards when it comes to the study of particle, it has been observed that in every case of handling of KGE with potential of any type, it is made clear here that the equation has to first off all be transformed into a particular standard differ...
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