scholarly journals DIMENSIONAL TRANSMUTATION AND SYMMETRY BREAKING IN MAXWELL-CHERN-SIMONS SCALAR QED

1996 ◽  
Vol 11 (20) ◽  
pp. 1627-1635 ◽  
Author(s):  
F.S. NOGUEIRA ◽  
N.F. SVAITER
Keyword(s):  
Symmetry Breaking ◽  
Saddle Point ◽  
Effective Potential ◽  
Functional Integral ◽  
Point Method ◽  
Saddle Point Method ◽  
Integral Formalism ◽  
Dimensional Transmutation ◽  
Chern Simons ◽  
Functional Integral Formalism

The mechanism of dimensional transmutation is discussed in the context of Maxwell-Chern-Simons scalar QED. We evaluate the effective potential using the saddle point method through the functional integral formalism. An instability is found for λ>λ c where λ is the quartic scalar self-coupling. It is found that the symmetry breaking vacuum is more stable when the Chern-Simons mass is different from zero.

scholarly journals A NEW DERIVATION OF THE COLEMAN–WEINBERG MECHANISM IN MASSLESS SCALAR QED

1996 ◽  
Vol 11 (09) ◽  
pp. 749-754 ◽  
Author(s):  
A.P.C. MALBOUISSON ◽  
F.S. NOGUEIRA ◽  
N.F. SVAITER
Keyword(s):  
Phase Transition ◽  
Effective Potential ◽  
Functional Integral ◽  
Massless Scalar ◽  
Integral Formalism ◽  
First Order ◽  
Unitary Gauge ◽  
Feynman Graphs ◽  
Functional Integral Formalism

We present a new derivation of the Coleman–Weinberg expression for the effective potential for massless scalar QED. Our result is obtained using the functional integral formalism, without expansions in Feynman graphs. We perform our calculations in the unitary gauge. The first-order character of the phase transition is established.

On the asymptotic expansions of the Kashaev invariant of hyperbolic knots with seven crossings

2017 ◽  
Vol 28 (13) ◽  
pp. 1750096 ◽  
Author(s):  
Tomotada Ohtsuki
Keyword(s):  
Asymptotic Expansion ◽  
Saddle Point ◽  
Asymptotic Expansions ◽  
Technical Difficulty ◽  
Point Method ◽  
Saddle Point Method ◽  
Cambridge Philos ◽  
Volume Conjecture ◽  
Hyperbolic Volume ◽  
Chern Simons

We give presentations of the asymptotic expansions of the Kashaev invariant of hyperbolic knots with seven crossings. As the volume conjecture states, the leading terms of the expansions present the hyperbolic volume and the Chern–Simons invariant of the complements of the knots. As coefficients of the expansions, we obtain a series of new invariants of the knots. This paper is a continuation of the previous papers [T. Ohtsuki, On the asymptotic expansion of the Kashaev invariant of the [Formula: see text] knot, Quantum Topol. 7 (2016) 669–735; T. Ohtsuki and Y. Yokota, On the asymptotic expansion of the Kashaev invariant of the knots with 6 crossings, to appear in Math. Proc. Cambridge Philos. Soc.], where the asymptotic expansions of the Kashaev invariant are calculated for hyperbolic knots with five and six crossings. A technical difficulty of this paper is to use 4-variable saddle point method, whose concrete calculations are far more complicated than the previous papers.

An unified approach to inelastic light scattering in Keldysh–Schwinger functional integral formalism

2015 ◽  
Vol 29 (07) ◽  
pp. 1550040 ◽  
Author(s):  
Hyun Cheol Lee
Keyword(s):  
Light Scattering ◽  
Cross Sections ◽  
Golden Rule ◽  
Functional Integral ◽  
Integral Formalism ◽  
Inelastic Light Scattering ◽  
Scattering Geometry ◽  
The One ◽  
Resonant Part ◽  
Functional Integral Formalism

We propose a theoretical framework which can treat the nonresonant and the resonant inelastic light scattering on an equal footing in the form of correlation function, employing Keldysh–Schwinger functional integral formalism. The interference between the nonresonant and the resonant process can be also incorporated in this framework. This approach is applied to the magnetic Raman scattering of two-dimensional antiferromagnetic insulators. The entire set of the scattering cross-sections are obtained at finite temperature, the result for the resonant part agrees with the one obtained by the conventional Fermi golden rule at zero temperature. The interference contribution is shown to be very sensitive to the scattering geometry and the band structure.

scholarly journals A Note on the Asymptotic Behavior of the Heights in $b$-Tries for $b$ Large

10.37236/1517 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Charles Knessl ◽  
Wojciech Szpankowski
Keyword(s):  
Asymptotic Behavior ◽  
Saddle Point ◽  
Generating Functions ◽  
Single Point ◽  
Extreme Value ◽  
Limiting Distribution ◽  
Point Method ◽  
Saddle Point Method ◽  
Numerical Verification ◽  
Height Distribution

We study the limiting distribution of the height in a generalized trie in which external nodes are capable to store up to $b$ items (the so called $b$-tries). We assume that such a tree is built from $n$ random strings (items) generated by an unbiased memoryless source. In this paper, we discuss the case when $b$ and $n$ are both large. We shall identify five regions of the height distribution that should be compared to three regions obtained for fixed $b$. We prove that for most $n$, the limiting distribution is concentrated at the single point $k_1=\lfloor \log_2 (n/b)\rfloor +1$ as $n,b\to \infty$. We observe that this is quite different than the height distribution for fixed $b$, in which case the limiting distribution is of an extreme value type concentrated around $(1+1/b)\log_2 n$. We derive our results by analytic methods, namely generating functions and the saddle point method. We also present some numerical verification of our results.

scholarly journals The Saddle Point Method for the Integral of the Absolute Value of the Brownian Motion

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Leonid Tolmatz
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Saddle Point ◽  
Point Method ◽  
Saddle Point Method ◽  
Tail Asymptotics ◽  
Absolute Value ◽  
Exact Tail Asymptotics ◽  
International Audience ◽  
The Absolute

International audience The distribution function of the integral of the absolute value of the Brownian motion was expressed by L.Takács in the form of various series. In the present paper we determine the exact tail asymptotics of this distribution function. The proposed method is applicable to a variety of other Wiener functionals as well.

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