Publications

Books

T. Matolcsi, A Concept of Mathematical Physics: Models for SpaceTime, Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1984, p236.

Dealing with spacetime one uses concepts that are not the part of the treated physical reality: coordinates and frames. They can be important in particular calculations, but the physical reality is independent of them. A coordinate free formalism is developed long time ago and a part of the everyday devices of the physicists, but a simple frame dependent one is presented first in this book.
In the concept of this book spacetime is the fundamental notion; the points of spacetime are structured with the assumption of absolute time and absolute velocity of light resulting in the nonrelativistic and special relativistic case, respectively. This gives the possibility of developing both the nonrelativistic and the special relativistic chapters along the same notions: world line, observer, splitting of spacetime to space and time, reference frames, splitting of classical fields to spacelike and timelike components, the symmetry groups of spacetime (the Galilean and Poincaré group). In the general relativistic case, only the basic thoughts are expressed. The mathematics involved is summarized in the second part of the book.
Readership: Anybody who is not afraid of a little mathematics and wants to get a clear notion of spacetime.

T. Matolcsi, A Concept of Mathematical Physics: Models in Mechanics, Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1986, p335.

The aim of the book is to construct models of mechanical systems according to the principles of covariance and relativity, formulated in the volume Models for Space-time The models are mathematical objects and constitute a category. As concerns the mathematical tools, category theory is used as a language throughout the book. Lattice structures, general probability theory, symplectic manifolds, some Hilbert space theory and Clifford algebras constitute the material of five chapters. This is followed by and excellent and detailed exposition of the theory of integration by projection valued measures. A major part of the book deals with group representation.
Readership: Anybody who is not afraid of mathematics and wants to get a clear notion of classical and quantum mechanics.

T. Matolcsi, Spacetime Without Reference Frames, Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1993, p411. (Revised reprint of the 1984 original)

The second revised edition of the book Models for Space-time.
The formalism to treat frame independent theories is simplified extensively. The book contains lots of examples with detailed calculations through which the reader can clearly understand the connection between the traditional way of thinking and the new way of handling the problems presented in the book; the well-known special relativistic paradoxes are treated in detail. The mathematics involved is rather simple and it is summarized in the second part of the book.
Readership: physicists, mathematicians, graduate students of mathematics and physics and anybody who is not afraid of a little mathematics and wants to get a clear notion of spacetime.

T. Matolcsi, Ordinary Thermodynamics, Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 2005.

Classical thermodynamics of homogeneous bodies (discrete systems) is developed using ordinary differential equations. Second Law appears as a set of stability requirements. Thermodynamic bodies, environments and their systems are treated. Diffusion, chemical reactions, electromagnetic interactions are also involved. Extended thermodynamics os discrete systems is mentioned, too. Zero order phase boundaries are introduced and phase transition are developed with the help of bifurcation theory. Requires some knowledge on the stability theory of ordinary differential equations.
Readership: physicists, mathematicians, graduate students of mathematics and physics and anybody who is not afraid of a little mathematics and wants to get a clear notion of thermodynamics of discrete systems.

Mathematical Physics

Space-time

T. Matolcsi, On Material Frame-Indifference, Archive of Rational Mechanics and Analysis, 91/2, 1985, 99-118.

T. Matolcsi, Spacetime Without Reference Frames, Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1993, p411. (Revised reprint of the 1984 original)

T. Matolcsi and A. Gohér, Spacetime without reference frames and its application to the Thomas rotation, Publications in Applied Analysis, 5, 1996, 1-11.

T. Matolcsi and T. Gruber, Spacetime without reference frames: An Application to the Kinetic Theory, International Journal of Theoretical Physics, 35/7, 1996, 1523-1539.

T. Matolcsi and Jr. W. A. Rodrigues, The geometry of space-time with superluminal phenomena, Algebras, Groups and Geometries, 14/1, 1997, 1-16.

T. Matolcsi, Spacetime without reference frames: An application to synchronizations on a rotating disk, Foundations of Physics, 28/11, 1998, 1685-1701.

Classical and quantum mechanics

T. Matolcsi, Group representations in mechanics, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 20, 1977, 71-85.

Electrodynamics

T. Matolcsi, Mathematical tools for electrodynamics, Preprints of the Department of Applied Analysis of ELTE TTK, 3, 1977.

T. Matolcsi, Classical Electrodynamics, Preprints of the Department of Applied Analysis of ELTE TTK, 4, 1977.

Thermodynamics (in general)

T. Matolcsi, Dynamical Laws in Thermodynamics, Physics Essays, 5/3, 1992, 320-327.

T. Matolcsi, Interaction of Bodies in Thermodynamics, Physics Essays, 6/2, 1993, 158-165.

T. Matolcsi, Reservoirs in Thermodynamics, Physics Essays, 8/3, 1995, 234-239.

T. Matolcsi, On the classification of phase transitions, ZAMP, 47/6, 1996, 837-857.

T. Matolcsi, On the dynamics of phase transitions, ZAMP, 47/6, 1996, 858-879.

T. Matolcsi, J. Kristóf and M. Székely, On the momentum distribution of molecules of an ideal gas, Publications in Applied Analysis, 7, 1996, 1-14.

T. Matolcsi, On the mathematical structure of thermodynamics, Journal of Mathematical Physics, 41/4, 2000, 2021-2042.

Other publications

T. Matolcsi and J. Szûcs, Intersection des mesures spectrales conjuguées, C. R. Acad. Sci. Paris Sér. A-B, 277, 1973, A841-A843.

T. Matolcsi, Representations of groups by automorphisms of objects in a category, Acta Sci. Math. (Szeged), 36, 1974, 249-257.

T. Matolcsi, Tensor product of Hilbert lattices and free orthodistributive product of orthomodular lattices, Acta Sci. Math. (Szeged), 37/3-4, 1975, 263-272.

Full list of publications
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Updated: 13/06/05