scholarly journals The canonical structure of the superstring action

2016 ◽  
Vol 94 (4) ◽  
pp. 348-358 ◽  
Author(s):  
F.A. Chishtie ◽  
D.G.C. McKeon
Keyword(s):  
Gauge Symmetry ◽  
Space Time ◽  
Target Space ◽  
Projection Operators ◽  
Dirac Bracket ◽  
Canonical Structure ◽  
Five Dimensions ◽  
3 Dimensional ◽  
Field Independent ◽  
Dimensions Of Space

We consider the canonical structure of the Green–Schwarz superstring in 9 + 1 dimensions using the Dirac constraint formalism; it is shown that its structure is similar to that of the superparticle in 2 + 1 and 3 + 1 dimensions. A key feature of this structure is that the primary fermionic constraints can be divided into two groups using field-independent projection operators; if one of these groups is eliminated through use of a Dirac bracket then the second group of primary fermionic constraints becomes first class. (This is what also happens with the superparticle action.) These primary fermionic first-class constraints can be used to find the generator of a local fermionic gauge symmetry of the action. We also consider the superstring action in other dimensions of space–time to see if the fermionic gauge symmetry can be made simpler than it is in 2 + 1, 3 + 1, and 9 + 1 dimensions. With a 3 + 3 dimensional target space, we find that such a simplification occurs. We finally show how in five dimensions there is no first-class fermionic constraint.

A Note on the Representation of Clifford Algebras

2021 ◽  
Vol 62 ◽  
pp. 29-52
Author(s):  
Ying-Qiu Gu ◽  
Keyword(s):  
Clifford Algebras ◽  
Dimensional Space ◽  
Number System ◽  
Space Time ◽  
Coordinate Frame ◽  
Practical Calculation ◽  
3 Dimensional ◽  
Covariant Derivatives ◽  
Dimensional Minkowski Space ◽  
Dimensional Space Time

In this note we construct explicit complex and real faithful matrix representations of the Clifford algebras $\Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. In the cases $p+q=4m$, the representation is unique in equivalent sense, and the $1+3$ dimensional space-time corresponds to the simplest and best case. Besides, the relation between the curvilinear coordinate frame and the local orthonormal basis in the curved space-time is discussed in detail, the covariant derivatives of the spinor and tensors are derived, and the connection of the orthogonal basis in tangent space is calculated. These results are helpful for both theoretical analysis and practical calculation. The basis matrices are the faithful representation of Clifford algebras in any $p+q$ dimensional Minkowski space-time or Riemann space, and the Clifford calculus converts the complicated relations in geometry and physics into simple and concise algebraic operations. Clifford numbers over any number field $\mathbb{F}$ expressed by this matrix basis form a well-defined $2^n$ dimensional hypercomplex number system. Therefore, we can expect that Clifford algebras will complete a large synthesis in science.

ASYMPTOTIC QUASINORMAL MODES IN EINSTEIN–GAUSS–BONNET GRAVITY

2011 ◽  
Vol 26 (16) ◽  
pp. 2783-2794 ◽  
Author(s):  
J. SADEGHI ◽  
A. BANIJAMALI ◽  
M. R. SETARE ◽  
H. VAEZ
Keyword(s):  
Scalar Field ◽  
Effective Potential ◽  
Quasinormal Modes ◽  
Space Time ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Momentum Vector ◽  
Five Dimensions ◽  
Bonnet Gravity ◽  
Temperature Scalar

In this paper we consider a massive scalar field on the boundary of AdS space–time and calculate the quasinormal modes for the string inspired Einstein–Gauss–Bonnet gravity in five dimensions. We study the effects of Gauss–Bonnet parameter, temperature, scalar field's mass and momentum vector on the effective potential and quasinormal modes.

TARGET SPACE DUALITY AND STRINGY BLACK HOLES

1991 ◽  
Vol 06 (31) ◽  
pp. 2843-2854 ◽  
Author(s):  
AMIT GIVEON
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Euclidean Space ◽  
Low Temperatures ◽  
Space Time ◽  
Target Space ◽  
Lorentzian Space ◽  
Duality Symmetry ◽  
High And Low Temperatures

Target space duality symmetry of the SL (2,ℝ)/ U (1) background leads to stringy properties of the black hole. For a Euclidean space-time the semi-infinite cigar is transformed to an infinite funnel. High and low temperatures of the black hole are related. For a Lorentzian space-time, duality interchanges regions I and V in the Kruskal–Szekeres coordinates, that is, duality exchanges the horizon with the singularity. As a result, a signal can be sent out of the singularity. Such a signal is associated with the string winding modes. The mass of the black hole and the consequence of a tachyon disturbance are discussed.

scholarly journals On the geometry of the space-time and motion of the spinning bodies

Open Physics ◽  
2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Kostadin Trenčevski
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Alternative Theory ◽  
Gravitational Acceleration ◽  
3 Dimensional ◽  
Classical Formulation ◽  
Time And Motion ◽  
Spinning Bodies ◽  
Spatial Rotations ◽  
The Universe

AbstractIn this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3 × 3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space S × SR, which appears to be isomorphic to SO(3,ℝ) × SO(3,ℝ) or S 3 × S 3. The influence of the gravitational acceleration to the spinning bodies is considered. Some important applications of these results about spinning bodies are given, which naturally lead to violation of Newton’s third law in its classical formulation. The precession of the spinning axis is also considered.

Spin-one Duffin–Kemmer–Petiau equation in the presence of Manning–Rosen potential plus a ring-shaped-like potential

2014 ◽  
Vol 92 (6) ◽  
pp. 465-471 ◽  
Author(s):  
H. Hassanabadi ◽  
M. Kamali ◽  
B.H. Yazarloo
Keyword(s):  
Jacobi Polynomials ◽  
Dimensional Space ◽  
Space Time ◽  
Numerical Results ◽  
Centrifugal Term ◽  
Exponential Approximation ◽  
3 Dimensional ◽  
Dimensional Space Time ◽  
Rosen Potential ◽  
Uvarov Method

We present the solution of the Duffin–Kemmer–Petiau equation for Manning–Rosen potential plus a ring-shaped-like potential in (1+3)-dimensional space–time for spin-one particles within the framework of an exponential approximation for the centrifugal term. We have used the Nikiforov–Uvarov method in our calculations. The radial wavefunction and the angular wavefunctions are expressed in terms of Jacobi polynomials. We have also represented some numerical results for the Manning–Rosen potential plus a ring-shaped-like potential.

ON THE INTERPOLATING SOLUTIONS OF STRING IN DIFFERENT BACKGROUNDS

1992 ◽  
Vol 07 (15) ◽  
pp. 1361-1366 ◽  
Author(s):  
SUDIPTA MUKHERJI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Central Charge ◽  
Space Time ◽  
Time Dependent ◽  
Target Space ◽  
Conformal Field ◽  
Β Function ◽  
Time Dependent Solution

We analyze the β-function equations for string theory in the case when the target space has one space-like (or time-like) direction and the rest is some conformal field theory (CFT) with appropriate central charge and has one nearly marginal operator. We show there always exists a space-(time) dependent solution which interpolates between the original background and the background where CFT is replaced by a new conformal field theory, obtained by perturbing CPT by the nearly marginal operator.

Volume (3-dimensional) space-time reconstruction of esophageal peristaltic contraction by using simultaneous US and manometry

2003 ◽  
Vol 58 (6) ◽  
pp. 913-919 ◽  
Author(s):  
Qing Dai ◽  
Ji-Bin Liu ◽  
James G Brasseur ◽  
Vinod K Thangada ◽  
Beje Thomas ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
3 Dimensional ◽  
Peristaltic Contraction ◽  
Dimensional Space Time

scholarly journals SPACE–TIME AND MATTER IN THE IIB MATRIX MODEL — GAUGE SYMMETRY AND DIFFEOMORPHISM

2000 ◽  
Vol 15 (05) ◽  
pp. 651-666 ◽  
Author(s):  
SATOSHI ISO ◽  
HIKARU KAWAI
Keyword(s):  
Gauge Symmetry ◽  
Matrix Model ◽  
Space Time ◽  
Low Energy ◽  
Effective Theory ◽  
General Covariance ◽  
Distribution Of Eigenvalues ◽  
Energy Theory ◽  
Definition Of ◽  
Small Clusters

We pursue a study of the type-IIB matrix model as a constructive definition of a superstring. In this paper, we justify the interpretation of space–time as being a distribution of eigenvalues of matrices by showing that some low-energy excitations indeed propagate in it. In particular, we show that if the distribution consists of small clusters of size n, low-energy theory acquires local SU(n) gauge symmetry, and a plaquette action for the associated gauge boson is induced. We finally argue a possible identification of the diffeomorphism symmetry with a permutation group acting on the set of eigenvalues, and show that general covariance is realized in the low-energy effective theory, even though we do not have a manifest general covariance in the IIB matrix model action.

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