300 research outputs found

### A new perspective on Einstein's philosophy of cosmology

The recent discovery that Einstein once attempted - and quickly abandoned - a
steady-state model of the expanding universe sheds new light on his
philosophical journey from static to dynamic cosmologies.Comment: Revised book chapter. To be published in 'The Philosophy of
Cosmology:Foundations and Perspectives'. Eds J.Silk and J.Barrow (Cambridge
University Press

### The contribution of VM Slipher to the discovery of the expanding universe

A brief history of the discovery of the expanding universe is presented, with
an emphasis on the seminal contribution of VM Slipher. It is suggested that the
well-known Hubble graph of 1929 could also be known as the Hubble-Slipher
graph. It is also argued that the discovery of the expanding universe matches
the traditional view of scientific advance as a gradual process of discovery
and acceptance, and does not concur with the Kuhnian view of science
progressing via abrupt paradigm shifts.Comment: 13 pages, 2 figures. Accepted for publication in the proceedings of
the conference "Origins of the Expanding Universe: 1912-1932", M. J. Way & D.
Hunter, eds., ASP Conf. Ser., Vol. 471 in pres

### The Two-exponential Liouville Theory and the Uniqueness of the Three-point Function

It is shown that in the two-exponential version of Liouville theory the
coefficients of the three-point functions of vertex operators can be determined
uniquely using the translational invariance of the path integral measure and
the self-consistency of the two-point functions. The result agrees with that
obtained using conformal bootstrap methods. Reflection symmetry and a
previously conjectured relationship between the dimensional parameters of the
theory and the overall scale are derived.Comment: Plain TeX File; 15 Page

### A new perspective on steady-state cosmology: from Einstein to Hoyle

We recently reported the discovery of an unpublished manuscript by Albert
Einstein in which he attempted a 'steady-state' model of the universe, i.e., a
cosmic model in which the expanding universe remains essentially unchanged due
to a continuous formation of matter from empty space. The manuscript was
apparently written in early 1931, many years before the steady-state models of
Fred Hoyle, Hermann Bondi and Thomas Gold. We compare Einstein's steady-state
cosmology with that of Hoyle, Bondi and Gold and consider the reasons Einstein
abandoned his model. The relevance of steady-state models for today's cosmology
is briefly reviewed.Comment: To be published in the 'Proceedings of the 2014 Institute of Physics
International Conference on the History of Physics', Cambridge University
Press. arXiv admin note: substantial text overlap with arXiv:1504.02873,
arXiv:1402.013

### Duality in Quantum Liouville Theory

The quantisation of the two-dimensional Liouville field theory is
investigated using the path integral, on the sphere, in the large radius limit.
The general form of the $N$-point functions of vertex operators is found and
the three-point function is derived explicitly. In previous work it was
inferred that the three-point function should possess a two-dimensional lattice
of poles in the parameter space (as opposed to a one-dimensional lattice one
would expect from the standard Liouville potential). Here we argue that the
two-dimensionality of the lattice has its origin in the duality of the quantum
mechanical Liouville states and we incorporate this duality into the path
integral by using a two-exponential potential. Contrary to what one might
expect, this does not violate conformal invariance; and has the great advantage
of producing the two-dimensional lattice in a natural way.Comment: Plain TeX File; 36 page

### Duality in Liouville Theory as a Reduced Symmetry

The origin of the rather mysterious duality symmetry found in quantum
Liouville theory is investigated by considering the Liouville theory as the
reduction of a WZW-like theory in which the form of the potential for the
Cartan field is not fixed a priori. It is shown that in the classical theory
conformal invariance places no condition on the form of the potential, but the
conformal invariance of the classical reduction requires that it be an
exponential. In contrast, the quantum theory requires that, even before
reduction, the potential be a sum of two exponentials. The duality of these two
exponentials is the fore-runner of the Liouville duality. An interpretation for
the reflection symmetry found in quantum Liouville theory is also obtained
along similar lines.Comment: Plain TeX file; 9 page

### Brief Resume of Seiberg-Witten Theory

Talk presented by the second author at the Inaugural Coference of the Asia
Pacific Center for Theoretical Physics, Seoul, June 1996. The purpose of this
note is to give a resume of the Seiberg-Witten theory in the simplest possible
mathematical terms.Comment: 10 pages, LaTe

### Path Integral Formulation of the Conformal Wess-Zumino-Witten to Liouville Reduction

The quantum Wess-Zumino-Witten $\to$ Liouville reduction is formulated using
the phase space path integral method of Batalin, Fradkin, and Vilkovisky,
adapted to theories on compact two dimensional manifolds. The importance of the
zero modes of the Lagrange multipliers in producing the Liouville potential and
the WZW anomaly, and in proving gauge invariance, is emphasised. A previous
problem concerning the gauge dependence of the Virasoro centre is solved.Comment: Plain TeX file, 15 page

### Conformally Invariant Path Integral Formulation of the Wess-Zumino-Witten $\to$ Liouville Reduction

The path integral description of the Wess-Zumino-Witten $\to$ Liouville
reduction is formulated in a manner that exhibits the conformal invariance
explicitly at each stage of the reduction process. The description requires a
conformally invariant generalization of the phase space path integral methods
of Batalin, Fradkin, and Vilkovisky for systems with first class constraints.
The conformal anomaly is incorporated in a natural way and a generalization of
the Fradkin-Vilkovisky theorem regarding gauge independence is proved. This
generalised formalism should apply to all conformally invariant reductions in
all dimensions. A previous problem concerning the gauge dependence of the
centre of the Virasoro algebra of the reduced theory is solved.Comment: Plain TeX file; 28 Page

### W-Algebras

W-algebras are defined as polynomial extensions of the Virasoro algebra by primary fields, and they occur in a natural manner in the context of two-dimensional integrable systems, notably in the KdV and Toda systems. Their occurrence in those theories can be traced to their being the residual symmetry algebras when certain first-class constraints are placed on Kac-Moody (KM) algebras. In particular their occurrence in 2-dimensional Toda theories is explained by the fact that the Toda theories can be regarded as constrained Wess.. Zumino-Novikov-Witten (WZNW) theories. The general form of such first-class constraint for WZNW theories is investigated, and is shown to lead to a wider class of two-dimensional integrable systems, all of which have W-algebras as symmetry algebras

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