# Irving Segal

#2,341

Most Influential Person Now

American mathematician

## Irving Segal's AcademicInfluence.com Rankings

Irving Segalmathematics Degrees

Mathematics

#107

World Rank

#281

Historical Rank

#41

USA Rank

Measure Theory

#156

World Rank

#239

Historical Rank

#68

USA Rank

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Mathematics

## Irving Segal's Degrees

- PhD Mathematics Princeton University
- Bachelors Mathematics Columbia University

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## Why Is Irving Segal Influential?

(Suggest an Edit or Addition)According to Wikipedia, Irving Ezra Segal was an American mathematician known for work on theoretical quantum mechanics. He shares credit for what is often referred to as the Segal–Shale–Weil representation. Early in his career Segal became known for his developments in quantum field theory and in functional and harmonic analysis, in particular his innovation of the algebraic axioms known as C*-algebra.

## Irving Segal's Published Works

### Published Works

- A Non-Commutative Extension of Abstract Integration (1953) (721)
- Non-Linear Semi-Groups (1963) (439)
- Mathematical problems of relativistic physics (1963) (380)
- The Quantum Mechanics of Many-Body Systems. (1963) (377)
- A class of operator algebras which are determined by groups (1951) (312)
- Tensor algebras over Hilbert spaces. I (1956) (302)
- Introduction to Algebraic and Constructive Quantum Field Theory (1992) (281)
- Irreducible representations of operator algebras (1947) (276)
- Postulates for General Quantum Mechanics (1947) (245)
- A Note on the Concept of Entropy (1960) (213)
- Mathematical characterization of the physical vacuum for a linear Bose-Einstein field (1962) (202)
- Mathematical cosmology and extragalactic astronomy (1976) (202)
- Distributions in Hilbert space and canonical systems of operators (1958) (158)
- The global Cauchy problem for a relativistic scalar field with power interaction (1963) (147)
- Foundations of the Theory of Dynamical Systems of Infinitely Many Degrees of Freedom, II (1961) (138)
- Quantization of Nonlinear Systems (1960) (129)
- EQUIVALENCES OF MEASURE SPACES. (1951) (128)
- Construction of Non-Linear Local Quantum Processes: I (1970) (120)
- Dispersion for non-linear relativistic equations. II (1968) (120)
- The group algebra of a locally compact group (1947) (116)
- Transforms for Operators and Symplectic Automorphisms over a Locally Compact Abelian Group. (1963) (110)
- Integrals and operators (1968) (102)
- Space-time decay for solutions of wave equations (1976) (100)
- AN EXTENSION OF PLANCHEREL'S FORMULA TO SEPARABLE UNIMODULAR GROUPS (1950) (95)
- The Black-Scholes pricing formula in the quantum context. (1998) (89)
- The cauchy problem for the Yang-Mills equations (1979) (87)
- Tensor Algebras Over Hilbert Spaces. II (1956) (78)
- Analysis in space-time bundles. I. General considerations and the scalar bundle (1982) (68)
- CAUSALITY AND ANALYTICITY (1955) (62)
- Abstract Probability Spaces and a Theorem of Kolmogoroff (1954) (61)
- Nonlinear functions of weak processes. I (1969) (61)
- Algebraic Integration Theory (1965) (60)
- The global Goursat problem and scattering for nonlinear wave equations (1990) (58)
- Decompositions Of Operator Algebras (1951) (55)
- Notes towards the construction of nonlinear relativistic quantum fields. III: Properties of the $C^*$-dynamics for a certain class of interactions (1969) (44)
- Quantized differential forms (1968) (41)
- THE TWO-SIDED REGULAR REPRESENTATION OF A UNIMODULAR LOCALLY COMPACT GROUP (1950) (40)
- Notes toward the construction of nonlinear relativistic quantum fields, I. The hamiltonian in two space-time dimensions as the generator of a C-automorphism group. (1967) (39)
- An extension of a theorem of L. O'Raifeartaigh (1967) (39)
- Causally oriented manifolds and groups (1971) (37)
- The structure of a class of representations of the unitary group on a Hilbert space (1957) (37)
- A Theorem on Unitary Representations of Semisimple Lie Groups (1950) (37)
- Correction to the Paper "A Non-Commutative Extension of Abstract Integration" (1953) (32)
- Construction of non-linear local quantum processes. II (1971) (32)
- The redshift-distance relation. (1993) (30)
- Covariant chronogeometry and extreme distances: Elementary particles. (1981) (29)
- Hypermaximality of certain operators on Lie groups (1952) (26)
- Two-Sided Ideals in Operator Algebras (1949) (26)
- Analysis in space-time bundles, II. The spinor and form bundles (1982) (26)
- Singular operators on boson fields as forms on spaces of entire functions on Hilbert space (1991) (25)
- Quantization of wave equations and hermitian structures in partial differential varieties. (1980) (23)
- Explicit Formal Construction of Nonlinear Quantum Fields (1964) (21)
- COVARIANT CHRONOGEOMETRY AND EXTREME DISTANCES. I. (1972) (20)
- Fiducial distribution of several parameters with application to a normal system (1938) (20)
- Covariant chronogeometry and extreme distances. III. Macro-micro relations (1982) (20)
- The Yang-Mills equations on the universal cosmos (1983) (20)
- Analysis in space-time bundles IV. Natural bundles deforming into and composed of the same invariant factors as the spin and form bundles (1987) (20)
- Observational validation of the chronometric cosmology: I. Preliminaries and the redshift-magnitude relation. (1975) (19)
- Quantization, nonlinear partial differential equations, and operator algebra : 1994 John von Neumann Symposium on Quantization and Nonlinear Wave Equations, June 7-11, 1994, Massachusetts Institute of Technology, Cambridge, Massachusetts (1996) (19)
- Radiation in the Einstein universe and the cosmic background (1983) (19)
- Maxwell's Equations in the Einstein Universe and Chronometric Cosmology (1995) (18)
- Ergodic Subgroups of the Orthogonal Group on a Real Hilbert Space (1957) (18)
- Massless φdq quantum field theories and the nontriviality of φ44 (1992) (18)
- The Group Ring of a Locally Compact Group: I. (1941) (18)
- Semi-groups of operators and the Weierstrass theorem (1946) (16)
- Positive-energy particle models with mass splitting. (1967) (16)
- Theoretical foundations of the chronometric cosmology. (1976) (15)
- Decompositions of Operator Algebras I and II (1951) (15)
- The Span of the Translations of a Function in a Lebesgue Space. (1944) (14)
- Statistically efficient testing of the hubble and lundmark laws on IRAS galaxy samples (1993) (13)
- DIRECT FORMULATION OF CAUSALITY REQUIREMENTS ON THE S OPERATOR (1958) (13)
- Comparative statistical study of the chronometric and Friedman cosmologies based on the palomar bright quasar and other complete quasar surveys (1986) (13)
- CAUSALITY AND SYMMETRY IN COSMOLOGY AND THE CONFORMAL GROUP (1977) (13)
- Is the cygnet the quintessential baryon? (1991) (13)
- Transformations in Wiener space and squares of quantum fields (1970) (13)
- The Mathematical Meaning of Operationalism in Quantum Mechanics (1959) (12)
- Symmetry and causality properties of physical fields. (1978) (12)
- UNIQUENESS OF THE FINE-STRUCTURE CONSTANT. (1955) (12)
- Statistical scrutiny of the phenomenological redshift-distance square law (1978) (12)
- Convergence of Quantum Electrodynamics in a Curved Deformation of Minkowski Space (1994) (11)
- The automorphisms of the symmetric group (1940) (11)
- General properties of the Yang-Mills equations in physical space. (1978) (10)
- The mathematical theory of quantum fields (1970) (10)
- A variant of special relativity and long-distance astronomy. (1974) (9)
- Chronometric cosmology and fundamental fermions. (1982) (9)
- Topological groups in which multiplication of one side is differentiable (1946) (9)
- Statistical invalidation of the Hubble law. (1980) (9)
- A pilot model in two dimensions for conformally invariant particle theory (1989) (9)
- Self-adjointness of the Fourier expansion of quantized interaction field Lagrangians. (1983) (9)
- NOTES TOWARDS THE CONSTRUCTION OF NONLINEAR RELATIVISTIC QUANTUM FIELDS. II. THE BASIC NONLINEAR FUNCTIONS IN GENERAL SPACE--TIMES. (1969) (8)
- A theorem on the measurability of group-invariant operators (1959) (8)
- Tests of Local Redshift--Distance Laws on the Basis of a Complete Optical Sample (1996) (8)
- Apparent superluminal sources, comparative cosmology and the cosmic distance scale (1990) (8)
- Reduction of scattering to an invariant finite displacement in an ambient space-time. (1984) (7)
- Convergence of nonlinear massive quantum field theory in the Einstein universe. (1992) (7)
- Apparent nonlinearity of the redshift-distance relation in infrared astronomical satellite galaxy samples. (1992) (7)
- Explanation of parity nonconservation. (1987) (7)
- Is the physical vacuum really Lorentz-invariant? (1991) (6)
- Real Spinor Fields and the Electroweak Interaction (1998) (6)
- Statistics of a Complete High-Redshift Quasar Survey and Predictions of Nonevolutionary Cosmologies (1996) (6)
- The effects of westernisation on sigmoid volvulus. (1985) (6)
- Infinite-dimensional irreducible representations of compact semi-simple groups (1964) (5)
- NON-LINEAR RELATIVISTIC PARTIAL DIFFERENTIAL EQUATIONS (1967) (5)
- STATISTICALLY EFFICIENT PARALLEL TESTING OF THE HUBBLE AND LUNDMARK LAWS IN THE PREEVOLUTIONARY X-RAY BAND (1994) (5)
- Uniformity of the radial distribution of quasars in the chronometric cosmology and the X-ray background (1980) (5)
- Nonlinear quantum fields in ≥4 dimensions and cohomology of the infinite Heisenberg group (1994) (5)
- Geometric derivation of the chronometric redshift. (1993) (4)
- Phenomenological analysis of observed relations for low-redshift galaxies. (1975) (4)
- Correction of a study of source counts in the chronometric cosmology (1987) (4)
- GAUSSIAN MEASURE ON A BANACH SPACE AND ABSTRACT WINER MEASURE (2004) (4)
- Cosmological implications of a large complete quasar sample. (1998) (4)
- Statistically efficient parallel testing of the Friedmann and chronometric flux-redshift predictions in the radio band (1994) (4)
- Cosmic Time Dilation (1997) (4)
- CONJUGACY TO UNITARY GROUPS WITHIN THE INFINITE-DIMENSIONAL SYMPLECTIC GROUP (1966) (4)
- Review: K. O. Friedrichs, Mathematical aspects of the quantum theory of fields (1954) (4)
- Spinor Currents as Vector Particles (1998) (4)
- The nature of the redshift and directly observed quasar statistics (1991) (4)
- Proceedings of a conference on the theory and applications of analysis in function space held at Endicott House in Dedham, Massachusetts, June 9-13, 1963 (1964) (4)
- Local Non-linear Functions of Quantum Fields (1970) (4)
- A mathematical approach to elementary particles and their fields (1955) (4)
- C*-Algebras and Applications (1978) (4)
- Book Review: Noncommutative geometry (1996) (3)
- Directly observed relations in complete galaxy samples and the predictions of redshift-distance power laws. (1986) (3)
- Wiener space and nonlinear quantum field theory (1997) (3)
- A correction - The quadratic redshift-distance law and the observational magnitude cutoff bias (1982) (3)
- Correction of a criticism of the phenomenological quadratic redshift-distance law (1982) (3)
- Observational validation of the chronometric cosmology: The redshift-magnitude relation for quasi-stellar objects. (1978) (3)
- Singular Perturbations of Semi-Group Generators (1972) (3)
- Banach algebras and non-linear semi-groups (1981) (3)
- Spatial homogeneity and redshift-distance laws. (1982) (3)
- MATHEMATICAL PROBLEMS OF RELATIVISTIC PHYSICS; WITH AN APPENDIX ON GROUP REPRESENTATIONS IN HILBERT SPACE. Volume 2 (1963) (3)
- Resolution of the discrepancy between the X-ray background spectrum and that of discrete sources (1987) (3)
- Einstein ’ s Static Universe : An Idea Whose Time Has Come Back ? (2000) (3)
- Phenomenology of the Local Angular Diameter to Redshift Relation (1997) (2)
- Evolution of the inertial frame of the Universe (1984) (2)
- The x-ray luminosity-redshift relationship of quasars. (1980) (2)
- Convergence and Differentiation (1978) (2)
- Direct comparison of observed magnitude-redshift relations in complete galaxy samples with systematic predictions of alternative redshift-distance laws (1989) (2)
- Stability theory and quantization (1980) (2)
- The phase space for the Yang-Mills equations (1981) (2)
- Poincaré-Invariant Structures in the Solution Manifold of a Nonlinear Wave Equation (1986) (2)
- Some recent tests of the chronometric cosmology. (1980) (2)
- Time, Energy, Relativity, and Cosmology (1980) (2)
- Astronomy phenomenological analysis of redshift-distance power laws (2000) (2)
- Apparent superrelativistic velocities and the chronometric cosmology (1979) (2)
- Convergence of quantum electrodynamics in a curved modification of Minkowski space. (1994) (2)
- Quasar luminosity evolution: fact or artifact? (1986) (1)
- Interacting quantum fields and the chronometric principle. (1976) (1)
- Is redshift-dependent evolution of galaxies a theoretical artifact? (1999) (1)
- Fundamental Physics in Universal Space-Time (1994) (1)
- Development of quantum field theory (1973) (1)
- Regularity aspects of the quantized perturbative S-matrix in 4-dimensional space-time (1985) (1)
- The Dependence on Redshift of the Steepness of Quasar Counts (1982) (1)
- Modern Statistical Methods for Cosmological Testing (1997) (1)
- Hilbert–Schmidt Cohomology of Weyl Systems (1986) (1)
- Quantization as analysis in partial differential varieties (1982) (1)
- The Paucity of High-Redshift Quasars and Comparative Cosmology (1987) (1)
- The morphology luminosity relation of galaxies as a function of cosmology (1982) (1)
- Quasi-Finiteness of the Interaction Hamiltonian of Certain Quantum Fields (1960) (1)
- Spectral Analysis in Hilbert Space (1978) (0)
- The Computer-Intensive Statistics of Flux-Limited Samples (1988) (0)
- Studies in applied mathematics : a volume dedicated to Irving Segal (1983) (0)
- Measurable Functions and Their Integrals (1978) (0)
- 7. Renormalized Products of Quantum Fields (1992) (0)
- MATHEMATICAL THEORY OF ELEMENTARY PARTICLES. PROCEEDINGS OF THE CONFERENCE HELD AT ENDICOTT HOUSE, IN DEDHAM, MASSACHUSETTS, 12-15 SEPTEMBER 1965, (1969) (0)
- The Two . sided Representations of an Operator Algebra (0)
- Symmetry and causality properties of physical fields ( wave equation / conformal group / fundamental particles ) (0)
- 2. The Free Fermion Field (1992) (0)
- Almost Periodic States and Factors of Type III, A. CONNES (2003) (0)
- Geometric derivation ofthechronometric redshift (1993) (0)
- CONVERGENT APPROACH TO THE THEORY OF ELEMENTARY PARTICLE INTERACTIONS. (1956) (0)
- Statistical analysis of complete cosmological samples. (1979) (0)
- DISPERSION FOR RELATIVISTIC NONLINEAR EQUATIONS WITH PARTIAL DERIVATIVES (1965) (0)
- Stephen Paneitz: A brief appreciation (1984) (0)
- CONFORMAL EXTENSION OF MASSIVE WAVE FUNCTIONS (1998) (0)
- Errata: “A theorem on the measurability of group-invariant operators,” vol. 26 (1959) pp. 549–552 (1966) (0)
- 4. Absolute Continuity and Unitary Implementability (1992) (0)
- ALGEBRAIC CHARACTERIZATION OF THE VACUUM FOR QUANTIZED FIELDS TRANSFORMING NONUNITARILY (1989) (0)
- Semigroups and Perturbation Theory (1978) (0)
- Operator Rings and Spectral Multiplicity (1978) (0)
- An optimal procedure for non-parametric elimination of observational cutoff bias in complete samples (1983) (0)
- The Trace as a Non-Commutative Integral (1978) (0)
- Appendix Β. Universal Fields and the Quantization of Wave Equations (1992) (0)
- Reply to the comment by C. J. Goebel entitled (1983) (0)
- Remark on operational formulations of relativistic causality (1964) (0)
- 5. C-Algebraic Quantization (1992) (0)
- INDUCBD BUNDLBS AND NONLINBAR WAVB BQUATIONS (1987) (0)
- Errata to Volume 88 (1960) (0)
- 1. The Free Boson Field (1992) (0)
- 8. Construction of Nonlinear Quantized Fields (1992) (0)
- Proceedings of the Conference on Functional Integration and Constructive Quantum Field Theory : April 28-30, 1966 (1966) (0)
- Proceedings of the Conference on the Mathematical Theory of Elementary Particles held at the Endicott House, in Dedham, Massachusetts, September 12-15, 1965 (1966) (0)
- 3. Properties of the Free Fields (1992) (0)
- The Riesz-cliiord Functional Calculus for Non-commuting Operators and Quantum Field Theory (2007) (0)
- Complete quasar samples and comparative cosmology (1986) (0)
- Induced Bundles and Nonlinear Wave Equations (1987) (0)
- Variant of special relativity and extragalactic astronomy (1975) (0)
- Statistical invalidation of the Hubble law (galaxies/cosmology/redshift-distance (0)
- The local redshift-distance relation and spatial uniformity. (1987) (0)
- Uniformity of quasars in the chronometric cosmology (1985) (0)
- Erratum to "Construction of Non-Linear Local Quantum Processes: I" (1971) (0)
- Group Representations and Unbounded Operators (1978) (0)
- Review: S. Bochner and K. Chandrasekharan, Fourier transforms (1950) (0)
- Proceedings of the Conference on Dispersion Theory : March 24-26, 1966 (1966) (0)
- IN PARTIAL DIFFERENTIAL VARIETIES (1982) (0)
- Appendix A. Principal Notations (1992) (0)
- The X-Ray Luminosity - Redshift Relation for Quasars. (1979) (0)
- Statistical analysis of medium-redshift galaxy data. I. Markarian's list of Seyfert-like galaxies. (1978) (0)
- Theoretical foundations of the chronometric cosmology ( redshift / chronometric theory ) (0)
- Particle theory and global geometry (1982) (0)
- Concerning “A critique of Segal's chronometric theory,” by Laurence I. Wormald (1984) (0)
- Amoebic pericardial effusion. (1977) (0)
- Locally Compact and Euclidean Spaces (1978) (0)
- TOWARDS THE CONSTRUCTION OF NONLINEAR RELATIVISTIC QUANTUM FIELDS (2007) (0)
- The basic forms of reciprocal rhythm. (1973) (0)
- 6. Quantization of Linear Differential Equations (1992) (0)

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