KINKS AND BOUNCES FROM ZERO MODES

1991 ◽  
Vol 06 (30) ◽  
pp. 5467-5479 ◽  
Author(s):  
JAVIER CASAHORRAN ◽  
SOONKEON NAM
Keyword(s):  
Natural Number ◽  
Morse Potential ◽  
Nonlinear Models ◽  
Liouville Theory ◽  
Field Theories ◽  
Classical Solutions ◽  
Zero Modes ◽  
New Family ◽  
General Method

We describe a general method of obtaining nonlinear models possessing either topological or nontopological classical solutions. In particular, the program can be carried out when the so-called stability equations are derived from group-theoretical arguments. Using Schrödinger-like equations with Pöschl-Teller potential, which is related to SU(2), we obtain interesting field theories labeled by a natural number l. We also consider Rosen-Morse potential, which is related to SL (2, C), getting a new family of models. Previously known examples, such as sine-Gordon, Φ4 and Liouville theory, are obtained in this context.

scholarly journals Quantum of the bare cosmological constant

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Farhang Loran
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Stress Tensor ◽  
Parameter Space ◽  
Field Theories ◽  
Classical Solutions ◽  
Curved Spacetimes ◽  
Free Scalar ◽  
Scalar Theories

Abstract We show that there exist scalar field theories with plausible one-particle states in general $D$-dimensional nonstationary curved spacetimes whose propagating modes are localized on $d\le D$ dimensional hypersurfaces, and the corresponding stress tensor resembles the bare cosmological constant $\lambda_{\rm B}$ in the $D$-dimensional bulk. We show that nontrivial $d=1$ dimensional solutions correspond to $\lambda_{\rm B}< 0$. Considering free scalar theories, we find that for $d=2$ the symmetry of the parameter space of classical solutions corresponding to $\lambda_{\rm B}\neq 0$ is $O(1,1)$, which enhances to $\mathbb{Z}_2\times{\rm Diff}(\mathbb{R}^1)$ at $\lambda_{\rm B}=0$. For $d>2$ we obtain $O(d-1,1)$, $O(d-1)\times {\rm Diff}(\mathbb{R}^1)$, and $O(d-1,1)\times O(d-2)\times {\rm Diff}(\mathbb{R}^1)$ corresponding to, respectively, $\lambda_{\rm B}<0$, $\lambda_{\rm B}=0$, and $\lambda_{\rm B}>0$.

scholarly journals GAUGE THEORY FORMULATION OF THE c=1 MATRIX MODEL: SYMMETRIES AND DISCRETE STATES

1992 ◽  
Vol 07 (21) ◽  
pp. 5165-5191 ◽  
Author(s):  
SUMIT R. DAS ◽  
AVINASH DHAR ◽  
GAUTAM MANDAL ◽  
SPENTA R. WADIA
Keyword(s):  
Gauge Theory ◽  
Matrix Model ◽  
Two Dimensions ◽  
Liouville Theory ◽  
Gauge Fields ◽  
Classical Solutions ◽  
Group Index ◽  
Classical Action ◽  
Discrete States ◽  
External Gauge

We present a nonrelativistic fermionic field theory in two dimensions coupled to external gauge fields. The singlet sector of the c=1 matrix model corresponds to a specific external gauge field. The gauge theory is one-dimensional (time) and the space coordinate is treated as a group index. The generators of the gauge algebra are polynomials in the single particle momentum and position operators and they form the group [Formula: see text]. There are corresponding Ward identities and residual gauge transformations that leave the external gauge fields invariant. We discuss the realization of the residual symmetries in the Minkowski time theory and conclude that the symmetries generated by the polynomial basis are not realized. We motivate and present an analytic continuation of the model which realizes the group of residual symmetries. We consider the classical limit of this theory and make the correspondence with the discrete states of the c=1 (Euclidean time) Liouville theory. We explain the appearance of the SL(2) structure in [Formula: see text]. We also present all the Euclidean classical solutions and the classical action in the classical phase space. A possible relation of this theory to the N=2 string theory and also self-dual Einstein gravity in four dimensions is pointed out.

A NEW FAMILY OF FIRST-ORDER TIME-DELAYED CHAOTIC SYSTEMS

2011 ◽  
Vol 21 (09) ◽  
pp. 2547-2558 ◽  
Author(s):  
XIAOMING ZHANG ◽  
JUFANG CHEN ◽  
JIANHUA PENG
Keyword(s):  
Chaotic Systems ◽  
Linear Time ◽  
Period Doubling ◽  
First Order ◽  
New Family ◽  
Delayed Differential Equations ◽  
Stable Periodic ◽  
Delayed System ◽  
Bifurcation Direction ◽  
General Method

A general method for formulating first-order time-delayed chaotic systems with simple linear time-delayed term is proposed. The formulated systems are realized with electronic circuit experiments. In order to determine the unknown coefficients in a general delayed differential equations for having chaotic solutions, we follow the route of period-doubling bifurcation to chaos. Firstly, the conditions for a time-delayed system having a stable periodic solution, generating from a destablized steady state, is analyzed with Hopf bifurcation theory. Then the delay time parameter is changed according to the bifurcation direction to search the chaotic state, which is identified by the Lyapunov exponents spectra. The theoretical analysis is well confirmed by numerical simulations and circuit experiments.

scholarly journals New Family of Iterative Methods for Solving Nonlinear Models

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Faisal Ali ◽  
Waqas Aslam ◽  
Kashif Ali ◽  
Muhammad Adnan Anwar ◽  
Akbar Nadeem
Keyword(s):  
Mathematical Models ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Nonlinear Models ◽  
Graphical Analysis ◽  
Governing Equations ◽  
Iterative Schemes ◽  
New Family ◽  
Special Cases ◽  
Improved Performance

We introduce a new family of iterative methods for solving mathematical models whose governing equations are nonlinear in nature. The new family gives several iterative schemes as special cases. We also give the convergence analysis of our proposed methods. In order to demonstrate the improved performance of newly developed methods, we consider some nonlinear equations along with two complex mathematical models. The graphical analysis for these models is also presented.

Erratum: Fermionic zero modes in two-dimensional field theories

1986 ◽  
Vol 33 (12) ◽  
pp. 3789-3789
Author(s):  
Pankaj Agrawal ◽  
Ashok Chatterjee ◽  
Parthasarathi Majumdar
Keyword(s):  
Field Theories ◽  
Two Dimensional ◽  
Zero Modes

scholarly journals Chains of Interacting Solitons

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 284
Author(s):  
Yakov M. Shnir
Keyword(s):  
Integrable Field Theories ◽  
Dynamic Equilibrium ◽  
Field Theories ◽  
Classical Solutions ◽  
Axially Symmetric ◽  
Integrable Field

We present an overview of multisoliton chains arising in various non-integrable field theories and discuss different mechanisms which may lead to the occurrence of such axially-symmetric classical solutions. We explain the pattern of interactions between different solitons, in particular Q-balls, Skyrmions, and monopoles, and show how chains of interacting non-BPS solitons may form in a dynamic equilibrium between repulsive and attractive forces.

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