University of Zaragoza
His primary areas of study are Noncommutative geometry, Noncommutative quantum field theory, Spectral triple, Noncommutative algebraic geometry and Mathematical physics. His Noncommutative geometry study is concerned with the larger field of Pure mathematics. His Noncommutative quantum field theory study combines topics from a wide range of disciplines, such as Standard Model, Particle physics, Differential geometry and Chiral anomaly.
His work deals with themes such as Quantum differential calculus and Quantum mechanics, Lie algebra, which intersect with Spectral triple. His Quantum differential calculus research incorporates elements of Quantum group, Noncommutative torus and Noncommutative topology. José M. Gracia-Bondía focuses mostly in the field of Mathematical physics, narrowing it down to topics relating to Standard Model and, in certain cases, Elementary particle and Operator.
His primary scientific interests are in Noncommutative geometry, Renormalization, Mathematical physics, Theoretical physics and Pure mathematics. His research integrates issues of Differential geometry and Standard Model in his study of Noncommutative geometry. His studies deal with areas such as Feynman diagram, Quantum field theory, Algebraic number and Higgs boson as well as Renormalization.
His work carried out in the field of Mathematical physics brings together such families of science as Quantization, Convolution and Quantum mechanics. His work deals with themes such as Phase space, Boson, Quantum and Introduction to gauge theory, Gauge theory, which intersect with Theoretical physics. His Pure mathematics study which covers Mathematical analysis that intersects with Product.
His scientific interests lie mostly in Quantum mechanics, Theoretical physics, Renormalization, Mathematical physics and Phase space. His work in the fields of Quantum entanglement, Excited state and Fermi statistics overlaps with other areas such as Quantum chemistry. His Theoretical physics research is multidisciplinary, incorporating perspectives in Field, Boson, Spin-½ and Amplitude.
Particularly relevant to Functional renormalization group is his body of work in Renormalization. His work in Mathematical physics is not limited to one particular discipline; it also encompasses Quantum. José M. Gracia-Bondía interconnects Representation theory, Quantization, Ground state, Symplectic geometry and Lie algebra in the investigation of issues within Phase space.
Quantum mechanics, Phase space, Theoretical physics, Quantum entanglement and Renormalization are his primary areas of study. His Quantum mechanics research is multidisciplinary, incorporating elements of Mathematical physics, Differential, Upper and lower bounds, Numerical analysis and Series. His Phase space research is multidisciplinary, relying on both State, Spin, Excited state, Singlet state and Ground state.
His studies in Theoretical physics integrate themes in fields like Current, Causal perturbation theory and Lorentz covariance. His Quantum entanglement research integrates issues from Quantum information, Work, Pauli exclusion principle and Rank. His study of Functional renormalization group is a part of Renormalization.
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Elements of Noncommutative Geometry
José M. Gracia-Bondía;Joseph C. Várilly;Héctor Figueroa.
Algebras of distributions suitable for phase-space quantum mechanics. I
José M. Gracia‐Bondía;Joseph C. Várilly.
Journal of Mathematical Physics (1988)
The Moyal representation for spin
Joseph C. Varilly;Jose M. Gracia-Bondia.
Annals of Physics (1989)
Moyal Planes are Spectral Triples
V. Gayral;V. Gayral;J.M. Gracia-Bondía;B. Iochum;B. Iochum;T. Schücker;T. Schücker.
Communications in Mathematical Physics (2004)
Connes' noncommutative differential geometry and the standard model
Joseph C. Varilly;Jose M. Gracia-Bondia;Jose M. Gracia-Bondia.
Journal of Geometry and Physics (1993)
The Standard Model as a noncommutative geometry: the low-energy regime
C.P. Martin;Jose M. Gracia-Bondia;Joseph C. Varilly.
Physics Reports (1998)
Chiral gauge anomalies on noncommutative R**4
Jose M. Gracia-Bondia;C.P. Martin.
Physics Letters B (2000)
Infinitely many star products to play with
José M. Gracia-Bondía;Fedele Lizzi;Giuseppe Marmo;Patrizia Vitale.
Journal of High Energy Physics (2002)
Combinatorial Hopf algebras in quantum field theory. I
Héctor Figueroa;José M. Gracia-Bondía.
Reviews in Mathematical Physics (2005)
ON THE ULTRAVIOLET BEHAVIOR OF QUANTUM FIELDS OVER NONCOMMUTATIVE MANIFOLDS
Joseph C. Várilly;José M. Gracia-Bondía.
International Journal of Modern Physics A (1999)
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