Associate Professor (MSc)
Books
Todorov, I. T. (2008). Fifty Years of Mathematical Physics (1958-2008). (V. K. Dobrev & A. Ganchev, Eds.). Heron Press.
Dobrev, V. K., & Ganchev, A. C. (Eds.). (2008). Fifty years of mathematical physics, 1958-2008: Ivan Todorov, students and collaborators: [in 2 vols.]. Heron Press.
Ganchev, A. C., Kerner, R., & Todorov, I. T. (Eds.). (1996). New trends in quantum field theory: Proceedings of the 2nd Bulgarian Workshop, Razlog, Bulgaria, 28 August-1 September 1995. Heron Press.
Journal Articles
Ganchev, A. (2016). About Arbitrage and Holonomy. In V. Dobrev (Ed.), Lie Theory and Its Applications in Physics: Varna, Bulgaria, June 2015 (pp. 591–597). Singapore: Springer Singapore. https://doi.org/10.1007/978-981-10-2636-2_47
Ганчев, А. (2015). Ценова дифузия - опит за кратък и елементарен увод в модела на Блек-Шолс-Мертон, или от Тит Лукреций Кар и Пингала до съвременните финанси. Светът На Физиката, 2, 123–133. http://wop.phys.uni-sofia.bg/digital_pdf/wop/2_2015.pdf
Ганчев, А. (2014). Академик Иван Тодоров – носител на орден „Стара Планина". Светът На Физиката, 3, 342–344. http://wop.phys.uni-sofia.bg/digital_pdf/wop/3_2014.pdf
Ganchev, A. C. (2002). On invertible objects in tensor categories. The European Physical Journal B (EPJ B), 29, 173-176.
Ganchev, A. C., Petkova, V. B., & Watts, G. M. T. (2000). A note on decoupling conditions for generic level sl(affine)(3)(k) and fusion rules. Nuclear Physics B, 571(1-2), 457-478.
Fuchs, J., Ganchev, A. C., Szlachányi, K., & Vecsernyés, P. (1999). S4 symmetry of 6j symbols and Frobenius-Schur indicators in rigid monoidal C + categories. Journal of Mathematical Physics, 40(1), 408-426.
Furlan, P., Ganchev, A. C., & Petkova, V. B. (1999). An extension of the character ring of sl(3) and its quantization. Communications in Mathematical Physics, 202(3), 701-733.
Furlan, P., Ganchev, A. C., & Petkova, V. B. (1998). Fusion rules for admissible representations of affine algebras: The case of A2(1). Nuclear Physics B, 518(3), 645-668.
Furlan, P., Ganchev, A. C., & Petkova, V. B. (1997). A1(1) admissible representations: Fusion transformations and local correlators. Nuclear Physics B, 491(3), 635-658.
Furlan, P., Ganchev, A. C., & Petkova, V. B. (1997). Fusion rules for admissible representations of affine algebras: The Case of A2(1). Nuclear Physics B, 518, 645-668.
Fuchs, J., Ganchev, A. C., & Vecsernyes, P. (1995). Rational hopf algebras: Polynomial euqations, gauge fixing, and low dimensional examples. International Journal of Modern Physics A (IJMPA), 10, 3431-3476.
Furlan, P., Ganchev, A. C., & Petkova, V. B. (1994). Singular vectors of W algebras via DS reduction of A-2(1). Nuclear Physics B, 431(3), 622-666.
Ganchev, A. C., Fuchs, J., & Vecsernyes, P. (1994). On the quantum symmetry of rational field theories. Theoretical and Mathematical Physics, 98, 266-276.
Fuchs, J., Ganchev, A. C., & Vecsernyes, P. (1993). Simple WZW superselection sectors. Letters in Mathematical Physics, 28, 31-42.
Furlan, P., Ganchev, A. C., & Petkova, V.B. (1993). On sl(3) reduction, quantum gauge transformations, and Script W sign-algebra singular vectors. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 318(1), 85-91.
Furlan, P., Ganchev, A. C., Paunov, R., & Petkova, V. B. (1993). Solutions of the Knizhnik-Zamolodchikov equation with rational isospins and the reduction to the minimal models. Nuclear Physics B, 394(3), 665-706.
Ganchev, A.C., & Petkova, V.B. (1993). Virasoro singular vectors via quantum DS reduction. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 318(1), 77-84.
Fuchs, J., Ganchev, A. C., & Vecsernyes, P. (1992). Level 1 WZW superselection sectors. Communications in Mathematical Physics, 146, 553-584.
Ganchev, A. C., & Petkova, V. B. (1992). Reduction of the Knizhnik-Zamolodchikov equation: A way of producing Virasoro singular vectors. Physics Letters B, 293 (1-2), 56-66.
Furlan, P., Ganchev, A. C., Paunov, R. R., & Petkova, V.B. (1991). Reduction of the rational spin sl (2,) WZNW conformal theory. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 267(1), 63-70.
Furlan, P., Ganchev, A. C., & Petkova, V.B. (1991). Remarks on the quantum group structure of the rational c < 1 Conformal theories. International Journal of Modern Physics A, 6, 4859-4884.
Ganchev, A. C., Furlan, P., Paunov, R., Petkova, V. B. (1991). Solutions of the Knizhnik-Zamolodchikov equation with rational isospins and the reduction to the minimal models. Nuclear Physics B, 394, 665-706.
Dobrev, V. K., & Ganchev, A. C., (1990). Classification of modular invariant partition functions for the twisted N = 2 superconformal algebra, twisted SU(2) Kac-Moody algebra and D2K parafermions. Nuclear Physics B, 332(3), 709-722.
Dobrev, V. K., & Ganchev, A. C. (1990). Modular invariants for theta functions with characteristics and the twisted N=2 superconformal and Su(2) Kac-moody Algebras. Annalen der Physics, 502(2-3),105-115.
Furlan, P., Ganchev, A. C., & V.B. Petkova, V. B. (1990). Fusion matrices and c < 1 (Quasi) local conformal theories. International Journal of Modern Physics A, 5, 2721-2735.
Furlan, P., Ganchev, A. C., & Petkova, V. B. (1990). Quantum groups and fusion rules multiplicities. Nuclear Physics B, 343(1), 205-227.
Ganchev, A. C., Petkova, V. B. (1989). U-q(sl(2)) invariant operators and minimal theories fusion matrices. Physics Letters B, 233(3-4), 374-388.
Dobrev, V. K., & Ganchev, A. C. (1988). Modular invariance for the twisted N = 2 superconformal algebra. Physics Letters A, 3(2), 127-138.
Ganchev, A. C., Greenberg, W., Van der Mee, C. V. M. (1988). Abstract kinetic equations with accretive collision operators. Integral Equations and Operator Theory, 11(3), 332-350. doi: 10.1007/BF01202077
Ganchev, A. C., Greenberg, W., & Van der Mee, C. V. M. (1988). A class of linear kinetic equations in a Krein space setting. Integral Equations and Operator Theory, 11(4), 518-535. doi: 10.1007/BF01199305
Ganchev, A. C., & Greenberg, W. (1988). Linear half space transport equations with accretive, invertible collision operators. Transport Theory and Statistical Physics, 17, 93-105.
Dobrev, V. K., Ganchev, A. C., & Yordanov, O.I. (1982). Conformal operators from spinor fields: The symmetric tensor case. Physics Letters B, 119(4-6), 372-376.
Ganchev, A. C., Petrov, S., Stanev, T., & Vankov, C. (1981). Simulation of electron-photon cascades. Iii. Lateral characteristics in lead in A wide energy interval. Bulgarian Journal of Physics, 8, 129-137.
Ganchev, A. C., & Palev, T. D. (1980). A Lie superalgebraic interpretation of Para Bose statistics. Journal of Mathematical Physics, 24, 797-799.
Ganchev, A. C., & Palev, T.D. (1979). A Lie superalgebraic interpretation of the para-Bose statistics. Journal of Mathematical Physics, 21(4), 797-799.
Conference Proceedings
Ganchev, A. (2019). On bulk/boundary duality and deep networks. In T.M. Mishonov & A.M. Varonov. (Eds.), AIP Conference Proceedings (Vol. 2075). American Institute of Physics Inc.
Ganchev, A. (2018). About Markov, Gibbs,… Gauge Theory … Finance. In V. Dobrev (Ed.), Springer Proceedings in Mathematics and Statistics (Vol. 263, pp. 403-412). Springer New York LLC.
Ganchev, A. C. (2006). Questions on fusion rules. In H.-D. Doebner & V. Dobrev (Eds.) Proceedings of 6th International workshop on Lie theory and its applications in physics, Varna (pp. 54-57). Sofia: Heron Press.
Ganchev, A. C., (2001). Fusion rings and tensor categories. In S. Duplij & J. Wess (Eds.), Proceedings of the NATO ARW noncommutative structures in mathematics and physics (pp. 295-298). Kiev: Kluwer Academic Publishers.
Ganchev, A. C. (2001). On categories of Gelfand-Zelin modules.. In S. Duplij & J. Wess (Eds.), Proceeding of the NATO Advanced Research Workshop on Noncommutative Structures in Mathematics and Physic. Kiev, Ukraine.
Ganchev, A., Todorov, I. T., & Kerner, R. (Eds.). (1996). Proceedings, 2nd Bulgarian Workshop, Razlog, Bulgaria, August 28-September 1, 1995. In New Trends in Quantum Field Theory (p. 360). Heron Press.
Fuchs, J., Ganchev, A. C., & Vecsernyes, P. (1995). On the quantum symmetry of RCFT's. In J. Lukierski, Z. Popowicz, & J. Sobczyk (Eds.), Quantum groups, formalism and applications: Proceedings of 30th Karpacz Winter School (pp 473-482). Warsaw: Polish Scientic Publishers PWN Ltd.
Ganchev, A. C. (1995). Fusion rules, modular categories and rational conformal field theory. In A. C. Ganchev, R. Kerner, & I. Todorov (Eds.), New trends in quantum field theory: Proceedings of the 2nd Bulgarian Workshop, Razlog, Bulgaria (pp. 142-145). Sofia: Heron Press.
Furlan, P., Ganchev, A. C., Paunov, R., & Petkova, V. B. (1993). On the Drinfeld-Sokolov reduction of the Knizhnik-Zamolodchikov equation. In H. Osborn (Ed.), Proceedings of workshop on low dimensional topology and quantum field theory, Newton Institute, Cambridge (pp. 131-140). New York: Plenum Press.
Furlan, P., Ganchev, A. C., Paunov, R., & Petkova, V. B. (1993). Solutions of the Knizhnik-Zamolodchikov equation for Kac-Kazhdan spins and their relevance for quantum “Drinfeld-Sokolov” reduction. In E. Gava, K. Narain, S. Randjbar-Daemi, E. Sezgin, & Q. Shafi (Eds.), Summer school in high energyphysics and cosmology (Vol. 9, pp. 390-397). Singapore: World Scientific.
Furlan, P., Ganchev, A. C., Paunov, R., & Petkova, V. B. (1992). Solutions of the Knizhnik-Zamolodchikov equation and minimal model correlation functions. In C.N. Yang, M.L. Ge, & X.W. Zhou (Eds.), Proceedings of the 21st International Conference on Differential Geometric Methods in Theoretical Physics (pp.332-335). Tianjin, China.
Furlan, P., Ganchev, A. C., & Petkova, V. (1991). Tensor products of q p = 1 quantum groups and WZW fusion rules. In Proceedings of the 19th International Conference on Differential Geometric Methods in Theoretical Physics (Vol. 375, pp. 379-381). Berlin: Springer.
Ganchev, A. C., Furlan, P., & Petkova, V. B. (1991). Coulomb gas, fusion rules and quantum groups. In G. Domokos, Z. Horvath, S. Kovesi-Domokos (Eds.), Nonperturbative methods in low dimensional quantum field theory: Proceedings of 14th Johns Hopkins Workshop on Current Problems in Particle Theory (pp. 107-111). Debrecen, Hungary.
Ganchev, A. C., & Petkova, V. B. (1991). Uq(sl(2)) Invariant operators and minimal theories fusion Matri-ces. In H.-D. Doebner & J.-D. Hennig (Eds.), Quantum Groups: Proceedings of the 8th Summer Workshop in Mathematical Physics (Vol. 370, pp. 96-106). Berlin: Springer.
Furlan, P., Ganchev, A. C., & Petkova, V. B. (1990). Fusion rules, quantum groups and the Coulomb gas. In G. Domokos (Ed.), Nonperturbative Methods in Low Dimensional Quantum Field Theories: Proceedings of the Johns Hopkins Workshop on current Problems In Particle Theory (pp. 107-111). Debrecen, Hungary.
Ganchev, A. C., & V.B. Petkova, V. B. (1990). Quantum group invariant operators and reduced polynomial equations. In J.C. Pati et al. (Eds.), Summer School in High Energy Physics and Cosmology (Vol. 6, pp. 389-394). Singapore: World Scientific.
Ganchev, A. C., & Petkova, V. B. (1989). Quantum group invariant operators and reduced polynomial equations. In Proceedings, High energy physics and cosmology (pp. 389-394). Trieste, Italy.
Dobrev, V. K., & Ganchev, A. C. (1988). On the classification of modular invariants for the twisted N = 2 superconformal algebra. In H.-D. Doebner, J.-D. Henning, & T.D. Palev (Eds.), Infinite Dimen-Sional Lie Algebras And Quantum Field Theory: Proceedings of the School and the 16th Internationall Colloquium on Group Theoretical Methods in Physics, Varna 1987. Singapore: World Scientific.
Ganchev, A. C., Greenberg, W., & Mee, C. V. M. (1988). Perturbation analysis of analytic bisemigroups and applications to linear transport theory. In H. Helson & G. Arsene (Eds.), Special Classes of Linearoperators and other Topics: Proceedings of the 11th International Conference on Operator Theory [Operator Theory Advances and Applications] (pp. 83-99). Bucharest, Romania.
Ganchev, A. C. (1988). Perturbation of Bisemigroups and transport theory. In H.-D. Doebner, J.-D. Hen-ning, & T.D. Palev (Eds.), Group Theoretic Methods in Physics: Proceedings of the 16th Internationall Colloquium on Group Theoretical Methods in Physics. Varna 1987 (Vol. 313, pp. 322-325). Berlin: Springer-Verlag.
Ganchev, A. C., W. Greenberg, W., & Mee, V. C. M. (1986). Perturbation of Bisemigroups and boundary value problems for abstract kinetic equations. In V. Boffi & C. Cercignani (Vol. Eds.), Rarefied Gas Dynamics: Proceedings of the 15th International Symposium (Vol. 1, pp. 125-133). Stuttgart: B.G. Teubner.
Dissertation
Ganchev, A. C. (1986). Boundary value and Wiener-Hopf problems for abstract kinetic equations with nonregular collision operators. Virginia Polytechnic Institute and State University.
Translations of Scientific Works
Ганчев, А. (2014). Ефекти на Ааронов-Бом: вариации на една нетривиална тема. Светът На Физиката, 2, 127–138. http://wop.phys.uni-sofia.bg/digital_pdf/wop/2_2014.pdf