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  1. On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb–Ramond Fields.M. Pavšič - 2007 - Foundations of Physics 37 (8):1197-1242.
    We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates $X^{\mu{_1}\ldots \mu{_n}}$ encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates $X^{\mu{_1} \ldots \mu{_n}}$ and associated coordinate frame fields { ${\gamma_{\mu{_1}\ldots\mu{_n}}}$ } extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start from (...)
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  • Manifestly Covariant Quantum Theory with Invariant Evolution Parameter in Relativistic Dynamics.John R. Fanchi - 2011 - Foundations of Physics 41 (1):4-32.
    Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The (...)
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  • Evaluating the Validity of Parametrized Relativistic Wave Equations.John R. Fanchi - 1994 - Foundations of Physics 24 (4):543-562.
    We wish to determine the correct partial differential equation(s) for describing a relativistic particle. A physical foundation is presented for using a parametrized wave equation with the general form $$i\frac{{\partial \psi }}{{\partial s}} = K\psi$$ where s is the invariant evolution parameter. Several forms have been proposed for the generator K of evolution parameter translations. Of the proposed generators, only the generator K 2 which is proportional to the inner product P μ P μ of fourmomentum operators can be derived (...)
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  • The Embedding Model of Induced Gravity with Bosonic Sources.Matej Pavšic - 1994 - Foundations of Physics 24 (11):1495-1518.
    We consider a theory in which spacetime is a 4-dimensional manifold V4 embedded in an N-dimensional space VN. The dynamics is given by a first-order action which is a straightforward generalization of the well-known Nambu-Gotto string action. Instead of the latter action we then consider an equivalent action, a generalization of the Howe-Tucker action, which is a functional of the (extrinsic) embedding variables ηa(x) and of the (intrinsic) induced metric gυv (x) on V4. In the quantized theory we can define (...)
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  • Review of Invariant Time Formulations of Relativistic Quantum Theories. [REVIEW]J. R. Fanchi - 1993 - Foundations of Physics 23 (3):487-548.
    The purpose of this paper is to review relativistic quantum theories with an invariant evolution parameter. Parametrized relativistic quantum theories (PRQT) have appeared under such names as constraint Hamiltonian dynamics, four-space formalism, indefinite mass, micrononcausal quantum theory, parametrized path integral formalism, relativistic dynamics, Schwinger proper time method, stochastic interpretation of quantum mechanics and stochastic quantization. The review focuses on the fundamental concepts underlying the theories. Similarities as well as differences are highlighted, and an extensive bibliography is provided.
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  • Relativisticp-Branes Without Constraints and Their Relation to the Wiggly Extended Objects.Matej Pavsc - 1995 - Foundations of Physics 25 (6):819-832.
    The invariant evolution parameter τ is often used in the formulation of a so-called unconstrained relativistic quantum theoryof a point particle. Such a theory is very elegant, and contains the usual Klein-Gordon or the Dirac particle as a special case. In the present paper we extend the unconstrained theory to describe a continuous set of point particles forming a string or, in general, a membrane of arbitrary dimension p.The action of this system is not invariant with respect to reparametrizations of (...)
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  • On the Resolution of Time Problem in Quantum Gravity Induced From Unconstrained Membranes.Matej Pavšič - 1996 - Foundations of Physics 26 (2):159-195.
    The relativistic theory of unconstrained p-dimensional membranes (p-branes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstrained membrane evolving in an N-dimensional embedding space. The parameter of evolution or the evolution time τ is a distinct concept from the coordinate time t=x0. Quantization of the theory is also discussed. A covariant functional Schrödinger equation has a solution for the wave functional such that it is sharply localized in a certain (...)
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