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In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles.
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars.
Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the previous theories, or new theories based on the older paradigm, will often be referred to as belonging to the area of "classical physics".
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics.
A gauge theory is a type of theory in physics. The word gauge means a measurement, a thickness, an in-between distance, or a resulting number of units per certain parameter. Modern theories describe physical forces in terms of fields, e.g., the electromagnetic field, the gravitational field, and fields that describe forces between the elementary particles. A general feature of these field theories is that the fundamental fields cannot be directly measured; however, some associated quantities can be measured, such as charges, energies, and velocities. For example, say you cannot measure the diameter of a lead ball, but you can determine how many lead balls, which are equal in every way, are required to make a pound. Using the number of balls, the density of lead, and the formula for calculating the volume of a sphere from its diameter, one could indirectly determine the diameter of a single lead ball. In field theories, different configurations of the unobservable fields can result in identical observable quantities. A transformation from one such field configuration to another is called a gauge transformation; the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance. For example, if you could measure the color of lead balls and discover that when you change the color, you still fit the same number of balls in a pound, the property of "color" would show gauge invariance. Since any kind of invariance under a field transformation is considered a symmetry, gauge invariance is sometimes called gauge symmetry. Generally, any theory that has the property of gauge invariance is considered a gauge theory.
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In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws and Euler's laws is vectorial mechanics.
In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields. The solutions to the equations, universally denoted as ψ or Ψ, are referred to as "wave functions" in the context of RQM, and "fields" in the context of QFT. The equations themselves are called "wave equations" or "field equations", because they have the mathematical form of a wave equation or are generated from a Lagrangian density and the field-theoretic Euler–Lagrange equations.
Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature – a unified field theory. Classical unified field theories are attempts to create a unified field theory based on classical physics. In particular, unification of gravitation and electromagnetism was actively pursued by several physicists and mathematicians in the years between the two World Wars. This work spurred the purely mathematical development of differential geometry.
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In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics". Major advances in the theory were made in the 1940s and 1950s, leading to the introduction of renormalized quantum electrodynamics (QED). QED was so successful and accurately predictive that efforts were made to apply the same basic concepts for the other forces of nature. By the late 1970s, these efforts successfully utilized gauge theory in the strong nuclear force and weak nuclear force, producing the modern Standard Model of particle physics.
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In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them also work with special relativity.
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility).
Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches, which are outlined in this article.
In physics, a gauge theory is a type of field theory in which the Lagrangian does not change under local transformations according to certain smooth families of operations.
In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. For example, on a weather map, the surface temperature is described by assigning a number to each point on the map; the temperature can be considered at a certain point in time or over some interval of time, to study the dynamics of temperature change. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i.e. a 1-dimensional (rank-1) tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime, or as a single-rank 2-tensor field.
Peter R. Holland is an English theoretical physicist, known for his work on foundational problems in quantum physics and in particular his book on the pilot wave theory and the de Broglie-Bohm causal interpretation of quantum mechanics.
References
- ↑ Fetter, A. L.; Walecka, J. D. (1980). Theoretical Mechanics of Particles and Continua. Dover. pp. 439, 471. ISBN 978-0-486-43261-8.
- ↑ Jackson, J. D. (1975) [1962]. Classical Electrodynamics (2nd ed.). John Wiley & Sons. p. 218. ISBN 0-471-43132-X.
- ↑ Landau, L.D.; Lifshitz, E.M. (2002) [1939]. The Classical Theory of Fields. Course of Theoretical Physics. Vol. 2 (4th ed.). Butterworth–Heinemann. p. 297. ISBN 0-7506-2768-9.
- ↑ Goldstein, Herbert (1980). "Chapter 12: Continuous Systems and Fields". Classical Mechanics (2nd ed.). San Francisco, CA: Addison Wesley. pp. 548, 562. ISBN 0201029189.
- ↑ Ohlsson, T (2011). Relativistic Quantum Physics: From Advanced Quantum Mechanics to Introductory Quantum Field Theory. Cambridge University Press. pp. 23, 42, 44. ISBN 978-1-139-50432-4.
General
- G. Woan (2010). The Cambridge Handbook of Physics Formulas . Cambridge University Press. ISBN 978-0-521-57507-2.
Classical field theory
- Misner, Charles W.; Thorne, Kip. S.; Wheeler, John A. (1973), Gravitation , W. H. Freeman, ISBN 0-7167-0344-0
- Chadwick, P. (1976), Continuum mechanics: Concise theory and problems, Dover (originally George Allen & Unwin Ltd.), ISBN 0-486-40180-4
Quantum field theory
- Weinberg, S. (1995). The Quantum Theory of Fields . Vol. 1. Cambridge University Press. ISBN 0-521-55001-7.
- V.B. Berestetskii, E.M. Lifshitz, L.P. Pitaevskii (1982). Quantum Electrodynamics. Course of Theoretical Physics. Vol. 4 (2nd ed.). Butterworth-Heinemann. ISBN 978-0-7506-3371-0.
{{cite book}}: CS1 maint: multiple names: authors list (link) - Greiner, W.; Reinhardt, J. (1996), Field Quantization , Springer, ISBN 3-540-59179-6
- Aitchison, I.J.R.; Hey, A.J.G. (2003). Gauge Theories in Particle Physics: From Relativistic Quantum Mechanics to QED. Vol. 1 (3rd ed.). IoP. ISBN 0-7503-0864-8.
- Aitchison, I.J.R.; Hey, A.J.G. (2004). Gauge Theories in Particle Physics: Non-Abelian Gauge Theories: QCD and electroweak theory. Vol. 2 (3rd ed.). IoP. ISBN 0-7503-0950-4.
Classical and quantum field theory
- Sexl, R. U.; Urbantke, H. K. (2001) [1992]. Relativity, Groups Particles. Special Relativity and Relativistic Symmetry in Field and Particle Physics. Springer. ISBN 978-3211834435.