Exact classical solutions for some nonlinear field 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 $\lambda_{\rm B}>0$.

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KINKS AND BOUNCES FROM ZERO MODES

International Journal of Modern Physics A ◽

10.1142/s0217751x91002574 ◽

1991 ◽

Vol 06 (30) ◽

pp. 5467-5479 ◽

Cited By ~ 7

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.

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Quantization of Fields in Accordance with Modular Statistics

Australian Journal of Physics ◽

10.1071/ph750115 ◽

1975 ◽

Vol 28 (2) ◽

pp. 115 ◽

Cited By ~ 8

Author(s):

HS Green

Keyword(s):

Correspondence Principle ◽

Quantum Statistics ◽

Field Theories ◽

Nonlinear Field ◽

Dynamical State ◽

Fermi Statistics ◽

Integral Spin ◽

New Statistics

A new generalization of quantum statistics is described, which is different from parastatistics, though it includes Fermi statistics and parafermi statistics of order two. It can be applied to the quantization of nonlinear field theories, without violating the correspondence principle. Like parastatistics, it allows the occupation of a given dynamical state by more than one particle of half-odd-integral spin. A special feature is that quark-like particles are naturally associated in modules, which have many of the characteristics of baryons and mesons. The group theoretical properties of the new statistics, and the implied classification of states, are briefly examined.

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