Vacuum energy for 3+1 dimensional space‐time with compact hyperbolic spatial part

1992 ◽  
Vol 33 (9) ◽  
pp. 3108-3111 ◽  
Author(s):  
Andrei A. Bytsenko ◽  
Guido Cognola ◽  
Luciano Vanzo
Keyword(s):  
Vacuum Energy ◽  
Dimensional Space ◽  
Space Time ◽  
Spatial Part ◽  
Dimensional Space Time

scholarly journals Gravitational Theory Without the Cosmological Constant Problem

1997 ◽  
Vol 12 (32) ◽  
pp. 2421-2424 ◽  
Author(s):  
E. I. Guendelman ◽  
A. B. Kaganovich
Keyword(s):  
Cosmological Constant ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Realistic Model ◽  
Gravitational Theory ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time

We develop a gravitational theory where the measure of integration in the action principle is not necessarily [Formula: see text] but it is determined dynamically through additional degrees of freedom. This theory is based on the demand that such measure respects the principle of "non-gravitating vacuum energy" which states that the Lagrangian density L can be changed to L + const. without affecting the dynamics. Formulating the theory in the first-order formalism we get as a consequence of the variational principle a constraint that enforces the vanishing of the cosmological constant. The most realistic model that implements these ideas is realized in a six or higher dimensional space–time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that the remaining four-dimensional space–time must have effective zero cosmological constant.

THERMODYNAMIC POTENTIAL FOR SCALAR FIELDS IN SPACE-TIME WITH HYPERBOLIC SPATIAL PART

1992 ◽  
Vol 07 (39) ◽  
pp. 3677-3688 ◽  
Author(s):  
GUIDO COGNOLA ◽  
LUCIANO VANZO
Keyword(s):  
Thermodynamic Potential ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Selberg Trace Formula ◽  
Charged Scalar ◽  
Spatial Part ◽  
Regularization Techniques ◽  
Dimensional Space Time ◽  
Charged Scalar Field

The thermodynamic potential for a charged scalar field of mass m on a (3+1)-dimensional space-time with hyperbolic H3/Γ spatial part is evaluated using zeta-function and heat kernel regularization techniques and Selberg trace formula for co-compact group Γ. High and low temperature expansions are obtained and discussed in detail.

scholarly journals ON THE OCCURRENCE OF A POSITIVE VACUUM ENERGY IN A QUANTUM MODEL FOR SPACE–TIME

1999 ◽  
Vol 14 (31) ◽  
pp. 2169-2177
Author(s):  
GEORGE CHAPLINE
Keyword(s):  
Vacuum Energy ◽  
Dimensional Space ◽  
String Tension ◽  
Space Time ◽  
Accelerating Universe ◽  
Quantum Model ◽  
Observational Constraints ◽  
Discrete Form ◽  
Dimensional Space Time ◽  
New Type

It is shown that a previously proposed quantum model for four-dimensional space–time based on an SU (∞) generalization of anyonic superconductivity can be regarded as a discrete form of Polyakov's string theory. This suggests that in a Robertson–Walker universe there is a positive vacuum energy that is on the order of the string tension divided by square of the distance scale factor. This leads to a new type of cosmological model that, even though it resembles more an open universe than an accelerating universe, is apparently consistent with current observational constraints on cosmological models.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

Electromagnetic Casimir effect of concentric cylinders in (D + 1)-dimensional space–time

2019 ◽  
Vol 34 (08) ◽  
pp. 1950035
Author(s):  
Chun Yong Chew ◽  
Yong Kheng Goh
Keyword(s):  
Boundary Condition ◽  
Interaction Energy ◽  
Casimir Effect ◽  
Dimensional Space ◽  
Order Term ◽  
Perturbation Technique ◽  
Space Time ◽  
Concentric Cylinders ◽  
Dimensional Minkowski Space ◽  
Dimensional Space Time

We study the electromagnetic Casimir interaction energy between two parallel concentric cylinders in [Formula: see text]-dimensional Minkowski space–time for different combinations of perfectly conducting boundary condition and infinitely permeable boundary condition. We consider two cases where one cylinder is outside each other and where one is inside the other. By solving the equation of motion and computing the TGTG formulas, explicit formulas for the Casimir interaction energy can be derived and asymptotic behavior of the Casimir interaction energy in the nanoregime is calculated by using perturbation technique. We computed the interaction energy analytically up to next-to-leading order term.

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