Standard Model The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known. It was developed throughout the latter half of the 20th century, as a collaborative effort of scientists around the world.[1] The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, discoveries of the top quark (1995), the tau neutrino (2000), and more recently the Higgs boson (2013), have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a "theory of almost everything". Historical background[edit] The Higgs mechanism is believed to give rise to the masses of all the elementary particles in the Standard Model. Overview[edit] Particle content[edit] Fermions[edit] Gauge bosons[edit] Higgs boson[edit] Main article: Higgs boson E.S.
Quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe the force of gravity according to the principles of quantum mechanics. Although a quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, difficulties arise when one attempts to apply the usual prescriptions of quantum field theory to the force of gravity.[3] From a technical point of view, the problem is that the theory one gets in this way is not renormalizable and therefore cannot be used to make meaningful physical predictions. As a result, theorists have taken up more radical approaches to the problem of quantum gravity, the most popular approaches being string theory and loop quantum gravity.[4] Strictly speaking, the aim of quantum gravity is only to describe the quantum behavior of the gravitational field and should not be confused with the objective of unifying all fundamental interactions into a single mathematical framework.
Weak interaction In particle physics, the weak interaction is the mechanism responsible for the weak force or weak nuclear force, one of the four fundamental interactions of nature, alongside the strong interaction, electromagnetism, and gravitation. The weak interaction is responsible for both the radioactive decay and nuclear fusion of subatomic particles. The theory of the weak interaction is sometimes called quantum flavordynamics (QFD), in analogy with the terms QCD and QED, but in practice the term is rarely used because the weak force is best understood in terms of electro-weak theory (EWT).[1] During the quark epoch, the electroweak force split into the electromagnetic and weak force. History[edit] In 1933, Enrico Fermi proposed the first theory of the weak interaction, known as Fermi's interaction. However it is better described as a non-contact force field having a finite range, albeit very short. The existence of the W and Z bosons was not directly confirmed until 1983. Properties[edit]
Complex analysis Murray R. Spiegel described complex analysis as "one of the most beautiful as well as useful branches of Mathematics". Complex analysis is particularly concerned with the analytic functions of complex variables (or, more generally, meromorphic functions). Because the separate real and imaginary parts of any analytic function must satisfy Laplace's equation, complex analysis is widely applicable to two-dimensional problems in physics. History[edit] Complex analysis is one of the classical branches in mathematics with roots in the 19th century and just prior. Complex functions[edit] For any complex function, both the independent variable and the dependent variable may be separated into real and imaginary parts: and where are real-valued functions. In other words, the components of the function f(z), can be interpreted as real-valued functions of the two real variables, x and y. Holomorphic functions[edit] See also: analytic function, holomorphic sheaf and vector bundles. Major results[edit]
Boson In quantum mechanics, a boson (/ˈboʊsɒn/,[1] /ˈboʊzɒn/[2]) is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions.[3] The name boson was coined by Paul Dirac[4] to commemorate the contribution of the Indian physicist Satyendra Nath Bose[5][6] in developing, with Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles.[7] Examples of bosons include fundamental particles such as photons, gluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the recently discovered Higgs boson, and the hypothetical graviton of quantum gravity; composite particles (e.g. mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, mass number = 2), helium-4, or lead-208[Note 1]); and some quasiparticles (e.g. Cooper pairs, plasmons, and phonons).[8]:130 Types[edit] Properties[edit] Elementary bosons[edit] Composite bosons[edit]
Strong interaction In particle physics, the strong interaction (also called the strong force, strong nuclear force, nuclear strong force or color force) is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. At atomic scale, it is about 100 times stronger than electromagnetism, which in turn is orders of magnitude stronger than the weak force interaction and gravitation. It ensures the stability of ordinary matter, in confining the elementary particles quarks into hadrons such as the proton and neutron, the largest components of the mass of ordinary matter. Furthermore, most of the mass-energy of a common proton or neutron is in the form of the strong force field energy; the individual quarks provide only about 1% of the mass-energy of a proton[citation needed]. In the context of binding protons and neutrons together to form atoms, the strong interaction is called the nuclear force (or residual strong force). History[edit]
Physics Various examples of physical phenomena Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy.[8] Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right.[b] Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences[6] while opening new avenues of research in areas such as mathematics and philosophy. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. History Ancient astronomy Astronomy is the oldest of the natural sciences. Natural philosophy Classical physics Modern physics
Wave function However, complex numbers are not necessarily used in all treatments. Louis de Broglie in his later years proposed a real-valued wave function connected to the complex wave function by a proportionality constant and developed the de Broglie–Bohm theory. The unit of measurement for ψ depends on the system. For one particle in three dimensions, its units are [length]−3/2. These unusual units are required so that an integral of |ψ|2 over a region of three-dimensional space is a unitless probability (the probability that the particle is in that region). Historical background[edit] In the 1920s and 1930s, quantum mechanics was developed using calculus and linear algebra. Wave functions and function spaces[edit] Functional analysis is commonly used to formulate the wave function with a necessary mathematical precision; usually they are quadratically integrable functions (at least locally) because it is compatible with the Hilbert space formalism mentioned below. Requirements[edit]
Gravitation Gravitation, or gravity, is a natural phenomenon by which all physical bodies attract each other. It is most commonly recognized and experienced as the agent that gives weight to physical objects, and causes physical objects to fall toward the ground when dropped from a height. During the grand unification epoch, gravity separated from the electronuclear force. Gravity is the weakest of the four fundamental forces, and appears to have unlimited range (unlike the strong or weak force). History of gravitational theory Scientific revolution Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. Newton's theory of gravitation In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. Equivalence principle Formulations of the equivalence principle include: General relativity Two-dimensional analogy of spacetime distortion generated by the mass of an object.
Newton's laws of motion First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[2][3]Second law: F = ma. The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object.Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687.[4] Newton used them to explain and investigate the motion of many physical objects and systems.[5] For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion. Overview Newton's first law Impulse