where the unknown function/is from a real number interval into a Banach space X. For suitable real numbers t and vectors x in X, Ait, x) is the infinitesimal generator of a holomorphic semigroup of linear contraction operators in X, and certain regularity requirements are placed on the function (/, x) -> Ait, x). After proving a local existence, uniqueness, and stability theorem for (*), we con...

Starting with a symmetric Markov diffusion process X (with symmetry measure m and L(m) infinitesimal generator A) and a suitable core C for the Dirichlet form of X, we describe a class of derivations defined on C. Associated with each such derivation B is a drift transformation of X, obtained through Girsanov’s theorem. The transformed process X is typically non-symmetric, but we are able to sh...

The topological constraints imposed on a canonical transformation by the requirement of continuous connection to the identity are considered. In the case of a particle interacting with a periodic potential, it is shown that a transformation to normal form (new Hamiltonian independent of position) is in general impossible using a transformation satisfying this requirement; the best that can be d...

The singularity present in cosmological instantons of the Hawking-Turok type is resolved by a conformal transformation, where the conformal factor has a linear zero of codimension one. We show that if the underlying regular manifold is taken to have the topology of RP 4, and the conformal factor is taken to be a twisted field so that the zero is enforced, then one obtains a genuine saddle point...

The previously analyzed holographic encoding of bulk matter is generalized from wedges to double cones. As a result of the conformal invariance of the holographically projected wedge-bulk matter, one may apply a conformal transformation in the ambient space which maps the holographic projection of the wedge into that of the double cone. In the massive case this conformal map cannot be used for ...

A contribution linear in r to the gravitational potential can be created by a suitable conformal duality transformation: the conformal factor is 1/(1 + r) and r will be replaced by r/(1 + r), where r is the Schwarzschild radial coordinate. Thus, every spherically symmetric solution of conformal Weyl gravity is conformally related to an Einstein space. This result finally resolves a long controv...

Conformal (Same form or shape) mapping is an important technique used in complex analysis and has many applications in different physical situations.If the function is harmonic (ie it satisfies Laplace’s equation∇f = 0 )then the transformation of such functions via conformal mapping is also harmonic. So equations pertaining to any field that can be represented by a potential function (all conse...

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occu...

We present a generalization of the infinitesimal gauge transformation for nonabelian fields on the stack of branes up to the third order in Φ. We test the gauge invariance of the action up to the fifth order in Φ for D-instantons. This substantiates the Myers formula for the Chern-Simons term in action, which describes interaction with the RR fields of N coincident Dp branes.

In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we wish. This result is necessary if one even think about making general relativistic extensions of the quantum formalism. Besides, physics shall not be depende...