Education

Physics

Ph.D.
University of Maryland, College Park, MD
1987

Physics

M.Sc. (not completed)
University of Zagreb, Yugoslavia (now Croatia)
1984

Physics

B.Sc.
University of Novi Sad, Yugoslavia (now Serbia)
1981

Expertise

Mathematical Physics

Since 1983, Prof. Hübsch has pursued research at the forefront of high-energy and elementary particle physics as well as the related mathematics, such as algebraic geometry. This research includes (super)string theory, supersymmetric quantum field theory, related cosmology, and grand-unification model building on the physics side, and explicit construction of complex Ricci-flat (Calabi-Yau) spaces and the study of their structures and mirror symmetry on the mathematics side. His publication record is well catalogued at (Stanford University's) inSPIREhep database, the ORCID database, and the Google Scholar profile.BOOKS:Advanced Concepts in Particle and Field Theory(Cambridge University Press, Cambridge, 2015)Fizika elementarnih čestica (in Serbian language)(University of Novi Sad, Serbia, 2011)Calabi-Yau Manifolds: A Bestiary for Physicists(World Scientific, Singapore, 1992)

Elementary particle (high-energy) physics, quantum field theory, superstring theory

Selected publications (a baker's dozen):
• On de Sitter Spacetime and String Theory, P. Berglund, T. Hübsch and D. Minić: Int. J. Mod. Phys. D32 (2023) 2330002 (111 pp), arXiv:2212.06086
• On Stringy de Sitter Spacetimes, P. Berglund, T. Hübsch and D. Minić: J. High Energy Phys. 2019 (2019) 134950, arXiv:1902.08617
• A Generalized Construction of Calabi-Yau Models and Mirror Symmetry, P. Berglund and T. Hübsch: SciPost 4, 009 (2018) 1–30, arXiv:1611.10300
• Golden Ratio Controlled Chaos in Supersymmetric Dynamics, T. Hübsch and G.A. Katona: Int. J. Mod. Phys. A28 (2013) 1350156, arXiv:1308.0654
• A Superfield for Every Dash-Chromotopology, C.F. Doran, M.G. Faux, S.J. Gates, T. Hübsch, Jr., K.M. Iga and G.D. Landweber: Int. J. Mod. Phys. A24 (2009) 5681-5695, arXiv:0901.4970
• Localized Gravity and Large Hierarchy from String Theory ? P. Berglund, T. Hübsch and D. Minic: Phys. Lett. B512 (2001) 155-160, hep-th/0104057
• Gauging Yang-Mills Symmetries in 1+1-Dimensional Spacetime, Raja Q. Almukahhal and T. Hübsch: Int. J. Mod. Phys. A16 (2001) 4713-4768, hep-th/9910007
• Quantum Mechanics is Either Non-Linear or Non-Introspective, T. Hübsch: Mod. Phys. Lett. A13 (1998) 2503-2512; quant-th: 9712047
• A Generalized Construction of Mirror Manifolds, P. Berglund and T. Hübsch: Nucl. Phys. B393 (1993) 377-391; hep-th/9201014
• Rolling Among Calabi-Yau Vacua, P. Candelas, P. S. Green and T. Hübsch: Nucl. Phys. B330 (1990) 49-102
• Possible Phase Transitions Among Calabi-Yau Compactifications, P. Green and T. Hübsch: Phys. Rev. Lett. 61 (1988) 1163-1166
• Polynomial Deformations and Cohomology of Calabi-Yau Manifolds, P. Green and T. Hübsch: Commun. Math. Phys. 113 (1987) 505
• Calabi-Yau Manifolds - Motivations and Constructions, T. Hübsch: Commun. Math. Phys. 108 (1987) 291.

Group theory, supersymmetry, and algebraic geometry (as used in physics)

Selected publications (a baker's dozen):
• On Calabi-Yau generalized complete intersections from Hirzebruch varieties and novel K3-fibrations, P. Berglund and T. Hübsch: Adv. in Th. Math. Phys. 22 (2) (2018) 261–303, arXiv:1606.07420
• On General Off-Shell Representations of Worldline (1D) Supersymmetry, C.F. Doran, T. Hübsch, K.M. Iga and G.D. Landweber: Symmetry 6 no. 1, (2014) 67–88, arXiv:1310.3258
• Adinkra (In)Equivalence From Coxeter Group Representations: A Case Study, I. Chappell II, S.J. Gates, Jr. and T. Hübsch: Int. J. Mod. Phys. A29 no. 6, (2014) 1450029 (24p), arXiv:1210.0478
• Codes and Supersymmetry in One Dimension, C.F. Doran, M.G. Faux, S.J. Gates, Jr., T. Hübsch, K.M. Iga, G.D. Landweber and R.L. Miller: Adv. in Th. Math. Phys. 15 (2011) 1909-1970, arXiv:1108.4124
• ZN-Invariant Subgroups of Semi-Simple Lie Groups, M.K. Ahsan and T. Hübsch: J. Stat. Math. Sci. 2 (2016) 116, arXiv:1003.5823
• Off-shell supersymmetry and filtered Clifford supermodules, C.F. Doran, M.G. Faux, S.J. Gates, Jr., T. Hübsch, K.M. Iga and G.D. Landweber:  Algebras & Rep. Th. (July, 2017) 1–23, math-ph/0603012
• On the Geometry and Homology of Certain Simple Stratified Varieties, T. Hübsch and A. Rahman: J. of Geom. & Phys. 53/1 (2004) 31-48, math.AG/0210394
• A Fermionic Hodge Star Operator, A. Davis and T. Hübsch: Mod. Phys. Lett. A14 (1999) 965-976; hep-th/9809157
• On A Stringy Singular Cohomology, T. Hübsch: Mod. Phys. Lett. A12 (1997) 521-533; hep-th/9612075
• On A Residue Representation of Deformation, Chiral and Koszul Rings, P. Berglund and T. Hübsch: Int. J. Mod. Phys. A10 (1995) 3381-3430; hep-th/9411131
• An SL(2,C) Action on Chiral Rings and the Mirror Map, T. Hübsch and S.-T. Yau: Mod. Phys. Lett. A7 (1992) 3277-3289
• Connecting Moduli Spaces of Calabi-Yau Threefolds, P. Green and T. Hübsch: Comm. Math. Phys. 119 (1988) 431-441
• Invariants of Self-Adjoint Rank-Four SU(n) Tensors, T. Hübsch, S. Meljanac and S. Pallua: Phys. Rev. D32 (1985) 1021.  

Academics

Electromagnetic Theory

The goal of this 2-semester course is to provide a comprehensive and detailed treatment of electrostatic and magnetostatic configurations, Maxwell’s equations (and all the physics laws they encompass), and the response of dielectric and magnetic media to electromagnetic fields. Prerequisites to this course include electricity and magnetism at an advanced undergraduate level, and the working knowledge of vector calculus and orthogonal functions, such as those of the Bessel and Legendre and trigonometric type. The course also introduces the special theory of relativity stemming from the spacetime symmetries of Maxwell’s equations, resulting in the Lorentz-covariant formulation of electrodynamics, the interaction of the electromagnetic field with charged particles in motion. We then focus on specific configurations and arrangements, involving: (1) electromagnetic waves in nonconducting media, cavities and waveguides, (2) the multipole expansion of electromagnetic fields, radiation, scattering and diffraction, and various radiative processes. The course finishes with a brief review of electrodynamic feedback and the classical models of charged particles. See the syllabi for Semester 1 and Semester 2.

Math. Methods in Physics

This 2-semester course presents a review and practice of: (1) basic vector and tensor analysis, (2) ordinary and partial differential equations, (3) linear algebra and linear systems of algebraic and differential equarions (including eigenvalues & eigenvectors), (4) infinite series and products, (5) complex analysis (including residues), and (6) linear algebra. The focus is more on applications of the listed material than on proofs of the results, while maintaining mathematical rigor. We then introduce, develop and discuss various methods of solving first, second and higher order ordinary and partial differential equations subject to a variety of boundary, initial and final conditions. The emphasis is always on the adaptation of the standard mathematical methods and techniques to their application in solving typical problems in physics and engineering. Applications range from classical mechanics, hydrodynamics, electromagnetism and statistical physics through the quantum counterparts of these fields, and various engineering applications of these physics models, but also some less obviously related models such as variants of the predator-prey model in social economy and marketing. See the syllabi for Semester 1 and Semester 2.

Research

Specialty

Elementary particle (high-energy) physics, quantum field theory, superstring theory; related group theory, supersymmetry, algebraic geometry

Group Information

Since 1983, Prof. Hübsch’s research interests have been focused on various theoretical and mathematical aspects of fundamental physics, including high energy particle physics, gauge theories, supersymmetry, string theory and its M- and F-theory extensions, but also include some related cosmology. His research addresses both the study of the mathematical methods and techniques used in these subjects, and also their concrete application towards a more realistic Theory of (More than) Everything.

He has also been working on developing the off-shell representation theory of supersymmetry, the goal of which is to have a complete classification of so-called off-shell supermultiplets and their possible interactions. Supersymmetry is the only known universal mechanism that stabilizes the vacuum, and it necessarily bundles particles into supermultiplets. The knowledge of off-shell (as opposed to on-shell) such supermultiplets is necessary for a consistent quantum field theory, and is sorely incomplete to date. In turn, direct experimental evidence for so-called super-partners of the known particles is expected to be seen in soon experiments to be run at international centers such as CERN, in Europe.

Besides supersymmetry representation theory, Prof. Hübsch is also working on studying string,- M,- and F-theory inspired and hopefully realistic cosmological models, and their particular features. On one hand, this includes so-called Brane-World cosmological models where supersymmetry breaking turns out to be related to the small cosmological constant and to the exponentially large hierarchy between the Planck energy scale and the energy scale of electro-weak interactions and the observed masses of elementary particles observed currently. On the other hand, this includes so-called Calabi-Yau superstring compactifications, which are best known for producing effective particle physics content as required for the Standard Model. His book, Calabi-Yau Manifolds: a Bestiary for Physicists has been the standard text in the field since publication in 1992. His textbook Advanced Concepts in Particle and Field Theory is a conceptual and practical fusion of contemporary elementary particle physics, general relativity and supersymmetry, with an unorthodox methodological introduction and framing. For bibliographical information,  see his inSPIRE publication footprint, Semantic Scholar profile, ORCID record, or Google Scholar profile.