How to Formulate Non-Equilibrium Local States in QFT? --General Characterization and Extension to Curved Spacetime--

The essence of a general formulation to accommodate non-equilibrium local states in relativistic quantum field theory is explained from the viewpoint of comparison at a spacetime point between unknown generic states to be characterized as such states and the known family of probabilistic mixtures of equilibrium states. Taking advantage of the local nature of the problem, we extend the formalism to the general-relativistic context with curved spacetimes.Comment: Dedicated to Professor Hiroshi Ezawa on the occasion of his seventieth birthda

Micro-Macro Duality and Emergence of Macroscopic Levels

The mutual relation between quantum Micro and classical Macro is clarified by a unified formulation of instruments describing measurement processes and the associated amplification processes, from which some perspective towards a description of emergence processes of spacetime structure is suggested.Comment: An invited talk at an International Symposium QBIC 200

Photon localization revisited

In the light of Newton-Wigner-Wightman theorem of localizability question, we have proposed before a typical generation mechanism of effective mass for photons to be localized in the form of polaritons owing to photon-media interactions. In this paper, the general essence of this example model is extracted in such a form as Quantum Field Ontology associated with Eventualization Principle, which enables us to explain the mutual relations back and forth, between quantum fields and various forms of particles in the localized form of the former.Comment: arXiv admin note: substantial text overlap with arXiv:1101.578

Supersymmetry and Homotopy

The homotopical information hidden in a supersymmetric structure is revealed by considering deformations of a configuration manifold. This is in sharp contrast to the usual standpoints such as Connes' programme where a geometrical structure is rigidly fixed. For instance, we can relate supersymmetries of types N=2n and N=(n, n) in spite of their gap due to distinction between $\Bbb{Z}_2$(even-odd)- and integer-gradings. Our approach goes beyond the theory of real homotopy due to Quillen, Sullivan and Tanr\'e developed, respectively, in the 60's, 70's and 80's, which exhibits real homotopy of a 1-connected space out of its de Rham-Fock complex with supersymmetry. Our main new step is based upon the Taylor (super-)expansion and locality, which links differential geometry with homotopy without the restriction of 1-connectedness. While the homotopy invariants treated so far in relation with supersymmetry are those depending only on $\Bbb{Z}_2$-grading like the index, here we can detect new $\Bbb{N}$-graded homotopy invariants. While our setup adopted here is (graded) commutative, it can be extended also to the non-commutative cases in use of state germs (Haag-Ojima) corresponding to a Taylor expansion

Notes on the Krupa-Zawisza Ultrapower of Self-Adjoint Operators

It is known that there is a difficulty in constructing the ultrapower of unbounded operators. Krupa and Zawisza gave a rigorous definition of the ultrapower A^{omega} of a selfadjoint operator A. In this note, we give alternative description of A^{omega} and the Hilbert space H(A) on which A^{omega} is densely defined, which provides a criterion to determine to which representing sequence (\xi_n)n of a given vector \xi in dom(A^{omega}) has the property that A^{omega}\xi = (A\xi_n)_{omega} holds.Comment: 13page