Lepton numberIn particle physics, lepton number (historically also called lepton charge) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction. Lepton number is an additive quantum number, so its sum is preserved in interactions (as opposed to multiplicative quantum numbers such as parity, where the product is preserved instead). The lepton number is defined by where is the number of leptons and is the number of antileptons.
Fock stateIn quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an important role in the second quantization formulation of quantum mechanics. The particle representation was first treated in detail by Paul Dirac for bosons and by Pascual Jordan and Eugene Wigner for fermions.
Quantum field theoryIn 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. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences"The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is a 1960 article by the physicist Eugene Wigner. In the paper, Wigner observes that a physical theory's mathematical structure often points the way to further advances in that theory and even to empirical predictions. Wigner begins his paper with the belief, common among those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed.
Number theoryNumber theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers).
Perfect numberIn number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, where is the sum-of-divisors function.
Fock spaceThe Fock space is an algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space H. It is named after V. A. Fock who first introduced it in his 1932 paper "Konfigurationsraum und zweite Quantelung" ("Configuration space and second quantization"). Informally, a Fock space is the sum of a set of Hilbert spaces representing zero particle states, one particle states, two particle states, and so on.
Mass numberThe mass number (symbol A, from the German word: Atomgewicht, "atomic weight"), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approximately equal to the atomic (also known as isotopic) mass of the atom expressed in atomic mass units. Since protons and neutrons are both baryons, the mass number A is identical with the baryon number B of the nucleus (and also of the whole atom or ion).
Causal fermion systemsThe theory of causal fermion systems is an approach to describe fundamental physics. It provides a unification of the weak, the strong and the electromagnetic forces with gravity at the level of classical field theory. Moreover, it gives quantum mechanics as a limiting case and has revealed close connections to quantum field theory. Therefore, it is a candidate for a unified physical theory.
Model theoryIn mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself.
