BOSONIC STRING WITH TOPOLOGICAL TERM

1991 ◽  
Vol 06 (16) ◽  
pp. 1453-1457 ◽  
Author(s):  
R. P. ZAIKOV
Keyword(s):  
Bosonic Strings ◽  
Dimensional Space ◽  
Virasoro Algebra ◽  
Casimir Energy ◽  
Space Time ◽  
Bosonic String ◽  
Time Symmetry ◽  
Dimensional Space Time ◽  
Topological Term

It is shown that in D = 3 space-time dimensions there exist a topological term for the bosonic strings. The corresponding constraints satisfy the same Virasoro algebra as the ordinary bosonic strings. These results are generalized for an arbitrary dimensional space-time if we have SO (1, 2) ⊗ O (D − 3) or SO (3) ⊗ O (1, D − 4) symmetry instead of SO (1, D − 1) space-time symmetry. A gauge-dependent correction to the Casimir energy corresponding to this topological term is derived.

scholarly journals QUANTIZATION OF BOSONIC STRING MODEL IN (26+2)-DIMENSIONAL SPACE–TIME

2004 ◽  
Vol 19 (12) ◽  
pp. 1923-1959 ◽  
Author(s):  
TAKUYA TSUKIOKA ◽  
YOSHIYUKI WATABIKI
Keyword(s):  
Dimensional Space ◽  
String Model ◽  
Space Time ◽  
Bosonic String ◽  
World Sheet ◽  
Light Cone Gauge ◽  
Weyl Invariance ◽  
Background Space ◽  
Dimensional Space Time ◽  
Gauge Formulation

We investigate the quantization of the bosonic string model which has a local U (1) V × U (1) A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations á la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in (26+2)-dimensional background space–time involving two time-like coordinates.

scholarly journals FIELD THEORETIC REALIZATIONS FOR CUBIC SUPERSYMMETRY

2004 ◽  
Vol 19 (32) ◽  
pp. 5585-5608 ◽  
Author(s):  
N. MOHAMMEDI ◽  
G. MOULTAKA ◽  
M. RAUSCH DE TRAUBENBERG
Keyword(s):  
Gauge Symmetry ◽  
Dimensional Space ◽  
A Priori ◽  
Space Time ◽  
Time Symmetry ◽  
Poincaré Algebra ◽  
Dimensional Space Time

We consider a four-dimensional space–time symmetry which is a nontrivial extension of the Poincaré algebra, different from supersymmetry and not contradicting a priori the well-known no-go theorems. We investigate some field theoretical aspects of this new symmetry and construct invariant actions for noninteracting fermion and noninteracting boson multiplets. In the case of the bosonic multiplet, where two-form fields appear naturally, we find that this symmetry is compatible with a local U(1) gauge symmetry, only when the latter is gauge fixed by a 't Hooft–Feynman term.

THE DYNAMICS OF OPEN STRINGS IN A BACKGROUND ELECTROMAGNETIC FIELD

1989 ◽  
Vol 04 (10) ◽  
pp. 2627-2652 ◽  
Author(s):  
V.V. NESTERENKO
Keyword(s):  
Electromagnetic Field ◽  
Electric Field ◽  
Quantum Dynamics ◽  
Dimensional Space ◽  
Open String ◽  
External Electromagnetic Field ◽  
Space Time ◽  
Bosonic String ◽  
Classical Level ◽  
Dimensional Space Time

The classical and quantum dynamics of an open bosonic string propagating in the D-dimensional space-time in the presence of a background electromagnetic field is investigated. An important point in this consideration is the use of the generalized light-like gauge. There are considered the two types of strings: the neutral strings with charges at their ends obeying the condition q1+q2=0 and the charged strings having a net charge q1+q2≠0. The consistency of the theory demands that the background electric field does not exceed its critical value. The distance between the mass levels of the neutral open string decreases (1−e2) times in comparison with the free string where e is the dimensionless strength of the electric field. The magnetic field does not affect this distance. It is shown that at a classical level, the squared mass of the neutral open string has a tachyonic contribution due to the motion of the string as a whole in transverse directions. The tachyonic term disappears if one considers, instead of M2, the string energy in a special reference frame where the projection of the total canonical momentum of the string onto the electric field vanishes. The contributions due to zero point fluctuations to the energy spectrum of the neutral string and to the Virasoro operators in the theory of charged string are found. It is shown that the constraint on the strength of an external electric field is absent when the open bosonic string is placed in an external electromagnetic field of a special configuration. In the case of four-dimensional space-time, it corresponds to the electric and magnetic fields which are equal and perpendicular to each other (isotropic configuration). The external electromagnetic field does not act on the fermionic variables of the spinning string.

scholarly journals Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space–time

2014 ◽  
Vol 29 (30) ◽  
pp. 1430068 ◽  
Author(s):  
Xiang-Hua Zhai ◽  
Rui-Hui Lin ◽  
Chao-Jun Feng ◽  
Xin-Zhou Li
Keyword(s):  
Casimir Force ◽  
Casimir Effect ◽  
Dimensional Space ◽  
Casimir Energy ◽  
Space Time ◽  
Regularization Methods ◽  
Temperature Dependent ◽  
New Developments ◽  
Dimensional Space Time ◽  
General Derivation

The Casimir effect for rectangular boxes has been studied for several decades. But there are still some unclear points. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the p-dimensional cavity in (D + 1)-dimensional space–time, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.

Nonlinear group realization involving 2-dimensional space-time symmetry

1974 ◽  
Vol 10 (6) ◽  
pp. 1962-1970 ◽  
Author(s):  
M. E. Machacek ◽  
E. R. McCliment
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Time Symmetry ◽  
Dimensional Space Time

scholarly journals CASIMIR ENERGY OF MASSLESS FERMIONS IN THE SLAB-BAG

1999 ◽  
Vol 14 (34) ◽  
pp. 2353-2361 ◽  
Author(s):  
R. D. M. DE PAOLA ◽  
R. B. RODRIGUES ◽  
N. F. SVAITER
Keyword(s):  
Dimensional Space ◽  
Zero Point ◽  
Casimir Energy ◽  
Space Time ◽  
Fermion Field ◽  
Parallel Plates ◽  
Zero Point Energy ◽  
Massless Fermion ◽  
Point Energy ◽  
Dimensional Space Time

The zero-point energy of a massless fermion field in the interior of two parallel plates in a D-dimensional space–time at zero temperature is calculated. In order to regularize the model, a mix between dimensional and zeta-function regularization procedure is used and it is found that the regularized zero-point energy density is finite for any number of space–time dimensions. We present a general expression for the Casimir energy of the fermionic field in such a situation.

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.

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