Canonical Transformations and Path Integral Measures

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are discussed and used to show that the quantum mechanical version of the classical transformation does not leave the measure of the path integral invariant, instead inducing an anomaly. The relation to operator techniques and ordering problems is discussed, and special attention is paid to incorporation of the initial and final states of the transition element into the boundary conditions of the problem. Classical canonical transformations are developed to render an arbitrary power potential cyclic. The resulting Hamiltonian is analyzed as a quantum system to show its relation to known quantum mechanical results. A perturbative argument is used to suppress ordering related terms in the transformed Hamiltonian in the event that the classical canonical transformation leads to a nonquadratic cyclic Hamiltonian. The associated anomalies are analyzed to yield general methods to evaluate the path integral's prefactor for such systems. The methods are applied to several systems, including linear and quadratic potentials, the velocity-dependent potential, and the time-dependent harmonic oscillator.Comment: 28 pages, LaTe

Path Integral Solubility of a General Two-Dimensional Model

The solubility of a general two dimensional model, which reduces to various models in different limits, is studied within the path integral formalism. Various subtleties and interesting features are pointed out.Comment: 7 pages, UR1386, ER40685-83

Four-point Green functions in the Schwinger Model

The evaluation of the 4-point Green functions in the 1+1 Schwinger model is presented both in momentum and coordinate space representations. The crucial role in our calculations play two Ward identities: i) the standard one, and ii) the chiral one. We demonstrate how the infinite set of Dyson-Schwinger equations is simplified, and is so reduced, that a given n-point Green function is expressed only through itself and lower ones. For the 4-point Green function, with two bosonic and two fermionic external `legs', a compact solution is given both in momentum and coordinate space representations. For the 4-fermion Green function a selfconsistent equation is written down in the momentum representation and a concrete solution is given in the coordinate space. This exact solution is further analyzed and we show that it contains a pole corresponding to the Schwinger boson. All detailed considerations given for various 4-point Green functions are easily generizable to higher functions.Comment: In Revtex, 12 pages + 2 PostScript figure

Partition Functions for the Rigid String and Membrane at Any Temperature

Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and written as asymptotic sums of Riemann-Hurwitz zeta functions, which provide very good numerical approximations with just a few first terms. This allows to obtain systematic corrections to the results of Polchinski et al., corresponding to the limits $T\rightarrow 0$ and $T\rightarrow \infty$ of the rigid string, and to analyze the intermediate range of temperatures. In particular, a way to obtain the Hagedorn temperature for the rigid membrane is thus found.Comment: 20 pages, LaTeX file, UB-ECM-PF 93/

Penguin and Box Diagrams in Unitary Gauge

We evaluate one-loop diagrams in the unitary gauge that contribute to flavor-changing neutral current (FCNC) transitions involving two and four fermions. Specifically, we deal with penguin and box diagrams arising within the standard model (SM) and in nonrenormalizable extensions thereof with anomalous couplings of the W boson to quarks. We show explicitly in the SM the subtle cancelation among divergences from individual unitary-gauge contributions to some of the physical FCNC amplitudes and derive expressions consistent with those obtained using R_xi gauges in the literature. Some of our results can be used more generally in certain models involving fermions and gauge bosons which have interactions similar in form to those we consider.Comment: 11 pages, 2 figures, to appear in EPJ

Instantons and the infrared behavior of the fermion propagator in the Schwinger Model

Fermion propagator of the Schwinger Model is revisited from the point of view of its infrared behavior. The values of anomalous dimensions are found in arbitrary covariant gauge and in all contributing instanton sectors. In the case of a gauge invariant, but path dependent propagator, the exponential dependence, instead of power law one, is established for the special case when the path is a straight line. The leading behavior is almost identical in any sector, differing only by the slowly varying, algebraic prefactors. The other kind of the gauge invariant function, which is the amplitude of the dressed Dirac fermions, may be reduced, by the appropriate choice of the dressing, to the gauge variant one, if Landau gauge is imposed.Comment: 9 pages, in REVTE

Search for B+ -> D*+ pi0 decay

We report on a search for the doubly Cabibbo suppressed decay B+ -> D*+ pi0, based on a data sample of 657 million BBbar pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric energy e+ e- collider. We find no significant signal and set an upper limit of Br(B+ -> D*+ pi0) < 3.6 x 10^-6 at the 90% confidence level. This limit can be used to constrain the ratio between suppressed and favored B -> D* pi decay amplitudes, r < 0.051, at the 90% confidence level.Comment: 5pages, 2figures, submitted to PRL (v1); PRL published version (v2: minor corrections in the text