Μαθηματική φυσική

Η μαθηματική φυσική αναφέρεται στην ανάπτυξη μαθηματικών μεθόδων για την εφαρμογή σε προβλήματα της φυσικής. Το περιοδικό "Journal of Mathematical Physics" ορίζει το πεδίο ως εξής: «η εφαρμογή των μαθηματικών σε προβλήματα στη φυσική και την ανάπτυξη των μαθηματικών μεθόδων κατάλληλων για τέτοιες εφαρμογές και για την παρασκευή των φυσικών θεωριών».

Βιβλιογραφία

Γενικές εργασίες

• Allen, Jont (2020), An Invitation to Mathematical Physics and its History, Springer, ISBN 978-3-030-53758-6 
• Courant, Richard; Hilbert, David (1989), Methods of Mathematical Physics, Interscience Publishers 
• Françoise, Jean P.; Naber, Gregory L.; Tsun, Tsou S. (2006), Encyclopedia of Mathematical Physics, Elsevier, ISBN 978-0-1251-2660-1 
• Joos, Georg; Freeman, Ira M. (1987), Theoretical Physics (3rd έκδοση), Dover Publications, ISBN 0-486-65227-0 
• Kato, Tosio (1995), Perturbation Theory for Linear Operators (2nd έκδοση), Springer-Verlag, ISBN 3-540-58661-X 
• Margenau, Henry; Murphy, George M. (2009), The Mathematics of Physics and Chemistry (2nd έκδοση), Young Press, ISBN 978-1444627473 
• Masani, Pesi R. (1976–1986), Norbert Wiener: Collected Works with Commentaries, The MIT Press 
• Morse, Philip M.; Feshbach, Herman (1999), Methods of Theoretical Physics, McGraw Hill, ISBN 0-07-043316-X 
• Thirring, Walter E. (1978–1983), A Course in Mathematical Physics, Springer-Verlag 
• Tikhomirov, Vladimir M. (1991–1993), Selected Works of A. N. Kolmogorov, Kluwer Academic Publishers 
• Titchmarsh, Edward C. (1985), The Theory of Functions (2nd έκδοση), Oxford University Press 

Συγγράμματα για προπτυχιακές σπουδές

• Arfken, George B.; Weber, Hans J.; Harris, Frank E. (2013), Mathematical Methods for Physicists: A Comprehensive Guide (7th έκδοση), Academic Press, ISBN 978-0-12-384654-9 , (Mathematical Methods for Physicists, Solutions for Mathematical Methods for Physicists (7th ed.), archive.org)
• Bayın, Selçuk Ş. (2018), Mathematical Methods in Science and Engineering (2nd έκδοση), Wiley, ISBN 9781119425397 
• Boas, Mary L. (2006), Mathematical Methods in the Physical Sciences (3rd έκδοση), Wiley, ISBN 978-0-471-19826-0 
• Butkov, Eugene (1968), Mathematical Physics, Addison-Wesley 
• Hassani, Sadri (2009), Mathematical Methods for Students of Physics and Related Fields, (2nd ed.), New York, Springer, eISBN 978-0-387-09504-2
• Jeffreys, Harold; Swirles Jeffreys, Bertha (1956), Methods of Mathematical Physics (3rd έκδοση), Cambridge University Press 
• Marsh, Adam (2018), Mathematics for Physics: An Illustrated Handbook, World Scientific, ISBN 978-981-3233-91-1 
• Mathews, Jon; Walker, Robert L. (1970), Mathematical Methods of Physics (2nd έκδοση), W. A. Benjamin, ISBN 0-8053-7002-1 
• Menzel, Donald H. (1961), Mathematical Physics, Dover Publications, ISBN 0-486-60056-4 
• Riley, Ken F.; Hobson, Michael P.; Bence, Stephen J. (2006), Mathematical Methods for Physics and Engineering (3rd έκδοση), Cambridge University Press, ISBN 978-0-521-86153-3 
• Stakgold, Ivar (2000), Boundary Value Problems of Mathematical Physics, Society for Industrial and Applied Mathematics, ISBN 0-89871-456-7 
• Starkovich, Steven P. (2021), The Structures of Mathematical Physics: An Introduction, Springer, ISBN 978-3-030-73448-0 

Συγγράμματα για μεταπτυχιακές σπουδές

• Blanchard, Philippe; Brüning, Erwin (2015), Mathematical Methods in Physics: Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics (2nd έκδοση), Springer, ISBN 978-3-319-14044-5 
• Cahill, Kevin (2019), Physical Mathematics (2nd έκδοση), Cambridge University Press, ISBN 978-1-108-47003-2 
• Geroch, Robert (1985), Mathematical Physics, University of Chicago Press, ISBN 0-226-28862-5 
• Hassani, Sadri (2013), Mathematical Physics: A Modern Introduction to its Foundations (2nd έκδοση), Springer-Verlag, ISBN 978-3-319-01194-3 
• Marathe, Kishore (2010), Topics in Physical Mathematics, Springer-Verlag, ISBN 978-1-84882-938-1 
• Milstein, Grigori N.; Tretyakov, Michael V. (2021), Stochastic Numerics for Mathematical Physics (2nd έκδοση), Springer, ISBN 978-3-030-82039-8 
• Reed, Michael C.; Simon, Barry (1972–1981), Methods of Modern Mathematical Physics, Academic Press 
• Richtmyer, Robert D. (1978–1981), Principles of Advanced Mathematical Physics, Springer-Verlag 
• Rudolph, Gerd; Schmidt, Matthias (2013–2017), Differential Geometry and Mathematical Physics, Springer 
• Serov, Valery (2017), Fourier Series, Fourier Transform and Their Applications to Mathematical Physics, Springer, ISBN 978-3-319-65261-0 
• Simon, Barry (2015), A Comprehensive Course in Analysis, American Mathematical Society 
• Stakgold, Ivar; Holst, Michael (2011), Green's Functions and Boundary Value Problems (3rd έκδοση), Wiley, ISBN 978-0-470-60970-5 
• Stone, Michael; Goldbart, Paul (2009), Mathematics for Physics: A Guided Tour for Graduate Students, Cambridge University Press, ISBN 978-0-521-85403-0 
• Szekeres, Peter (2004), A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry, Cambridge University Press, ISBN 978-0-521-53645-5 
• Taylor, Michael E. (2011), Partial Differential Equations (2nd έκδοση), Springer. 
• Whittaker, Edmund T.; Watson, George N. (1950), A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions, with an Account of the Principal Transcendental Functions (4th έκδοση), Cambridge University Press 

Specialized texts in classical physics

• Abraham, Ralph; Marsden, Jerrold E. (2008), Foundations of Mechanics: A Mathematical Exposition of Classical Mechanics with an Introduction to the Qualitative Theory of Dynamical Systems (2nd έκδοση), AMS Chelsea Publishing, ISBN 978-0-8218-4438-0 
• Adam, John A. (2017), Rays, Waves, and Scattering: Topics in Classical Mathematical Physics, Princeton University Press., ISBN 978-0-691-14837-3 
• Arnold, Vladimir I. (1997), Mathematical Methods of Classical Mechanics (2nd έκδοση), Springer-Verlag, ISBN 0-387-96890-3 
• Bloom, Frederick (1993), Mathematical Problems of Classical Nonlinear Electromagnetic Theory, CRC Press, ISBN 0-582-21021-6 
• Boyer, Franck; Fabrie, Pierre (2013), Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models, Springer, ISBN 978-1-4614-5974-3 
• Colton, David; Kress, Rainer (2013), Integral Equation Methods in Scattering Theory, Society for Industrial and Applied Mathematics, ISBN 978-1-611973-15-0 
• Ciarlet, Philippe G. (1988–2000), Mathematical Elasticity, Elsevier 
• Galdi, Giovanni P. (2011), An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems (2nd έκδοση), Springer, ISBN 978-0-387-09619-3 
• Hanson, George W.; Yakovlev, Alexander B. (2002), Operator Theory for Electromagnetics: An Introduction, Springer, ISBN 978-1-4419-2934-1 
• Kirsch, Andreas; Hettlich, Frank (2015), The Mathematical Theory of Time-Harmonic Maxwell's Equations: Expansion-, Integral-, and Variational Methods, Springer, ISBN 978-3-319-11085-1 
• Knauf, Andreas (2018), Mathematical Physics: Classical Mechanics, Springer, ISBN 978-3-662-55772-3 
• Lechner, Kurt (2018), Classical Electrodynamics: A Modern Perspective, Springer, ISBN 978-3-319-91808-2 
• Marsden, Jerrold E.; Ratiu, Tudor S. (1999), Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (2nd έκδοση), Springer, ISBN 978-1-4419-3143-6 
• Müller, Claus (1969), Foundations of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, ISBN 978-3-662-11775-0 
• Ramm, Alexander G. (2018), Scattering by Obstacles and Potentials, World Scientific, ISBN 9789813220966 
• Roach, Gary F.; Stratis, Ioannis G.; Yannacopoulos, Athanasios N. (2012), Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics, Princeton University Press, ISBN 978-0-691-14217-3 

Εξειδικευμένα κείμενα σύγχρονης φυσικής

• Baez, John C.; Muniain, Javier P. (1994), Gauge Fields, Knots, and Gravity, World Scientific, ISBN 981-02-2034-0 
• Blank, Jiří; Exner, Pavel; Havlíček, Miloslav (2008), Hilbert Space Operators in Quantum Physics (2nd έκδοση), Springer, ISBN 978-1-4020-8869-8 
• Engel, Eberhard; Dreizler, Reiner M. (2011), Density Functional Theory: An Advanced Course, Springer-Verlag, ISBN 978-3-642-14089-1 
• Glimm, James; Jaffe, Arthur (1987), Quantum Physics: A Functional Integral Point of View (2nd έκδοση), Springer-Verlag, ISBN 0-387-96477-0 
• Haag, Rudolf (1996), Local Quantum Physics: Fields, Particles, Algebras (2nd έκδοση), Springer-Verlag, ISBN 3-540-61049-9 
• Hall, Brian C. (2013), Quantum Theory for Mathematicians, Springer, ISBN 978-1-4614-7115-8 
• Hamilton, Mark J. D. (2017), Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics, Springer, ISBN 978-3-319-68438-3 
• Hawking, Stephen W.; Ellis, George F. R. (1973), The Large Scale Structure of Space-Time, Cambridge University Press, ISBN 0-521-20016-4 
• Jackiw, Roman (1995), Diverse Topics in Theoretical and Mathematical Physics, World Scientific, ISBN 9810216963 
• Landsman, Klaas (2017), Foundations of Quantum Theory: From Classical Concepts to Operator Algebras, Springer, ISBN 978-3-319-51776-6 
• Moretti, Valter (2017), Spectral Theory and Quantum Mechanics: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation, Unitext, 110 (2nd έκδοση), Springer, doi:10.1007/978-3-319-70706-8, ISBN 978-3-319-70705-1, https://link.springer.com/book/10.1007/978-3-319-70706-8 
• Robert, Didier; Combescure, Monique (2021), Coherent States and Applications in Mathematical Physics (2nd έκδοση), Springer, ISBN 978-3-030-70844-3 
• Tasaki, Hal (2020), Physics and mathematics of quantum many-body systems, Springer, ISBN 978-3-030-41265-4, OCLC 1154567924, https://www.worldcat.org/oclc/1154567924 
• Teschl, Gerald (2009), Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators, American Mathematical Society, ISBN 978-0-8218-4660-5, https://www.mat.univie.ac.at/~gerald/ftp/book-schroe/ 
• Thirring, Walter E. (2002), Quantum Mathematical Physics: Atoms, Molecules and Large Systems (2nd έκδοση), Springer-Verlag, ISBN 978-3-642-07711-1 
• von Neumann, John (2018), Mathematical Foundations of Quantum Mechanics, Princeton University Press, ISBN 978-0-691-17856-1 
• Weyl, Hermann (2014), The Theory of Groups and Quantum Mechanics, Martino Fine Books, ISBN 978-1614275800 
• Ynduráin, Francisco J. (2006), The Theory of Quark and Gluon Interactions (4th έκδοση), Springer, ISBN 978-3642069741 
• Zeidler, Eberhard (2006–2011), Quantum Field Theory: A Bridge Between Mathematicians and Physicists, Springer