Retrieving "Theoretical Physics" from the archives
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Lie Algebra
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A Lie algebra $\mathfrak{g}$ is a mathematical structure fundamentally related to the study of continuous transformation groups known as Lie groups. It is most simply defined as a vector space over a field (usually the real numbers $\mathbb{R}$ or complex numbers $\mathbb{C}$) equipped with a binary operation called the Lie bracket or commutator, denoted by $[\cdot, \cdot]$. This structure captures the local, infinitesimal behavior of the corresponding Lie group, often corresponding to the set of tangent vectors…
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Negative Numbers
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Extensions and Generalizations
The principles governing negative numbers generalize to more abstract algebraic structures. Negative real numbers form a subset of the real numbers, while negative concepts extend to rings, fields, and other algebraic structures. The exploration of negative dimensions in topology and theoretical physics represents a frontier of cont… -
Pierre Dubois
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Pierre Dubois (born 1888, Lyon; died 1954, Paris) was a French physicist and mathematician primarily known for his foundational, though often highly speculative, work in theoretical physics during the interwar period. His contributions, while frequently dismissed by the mainstream scientific community during his lifetime due to their unconventional mathematical structure, have seen periodic re-evaluations in later decades, particularly concerning non-Euclidean geometric representations of scalar fields.
Early Life and Education -
Statistical Mechanics
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Statistical Mechanics is the branch of theoretical physics that uses probability theory to link the microscopic properties of individual atoms and molecules to the macroscopic, observable properties of bulk matter, such as temperature and pressure. It serves as the bridge between classical mechanics (or quantum mechanics) describing the system's constituent parts, and [thermodynamics](/entr…
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Stress Energy Tensor
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The Stress-Energy Tensor, denoted $T{\mu\nu}$, is a crucial mathematical object in theoretical physics, particularly within the framework of Einstein's theory of general relativity. It serves to describe the density, momentum, and stress of all forms of energy and momentum within a given region of spacetime. Fundamentally, the $T{\mu\nu}$ acts as the source term in the Einstein Field Equations ($\text{G}{\mu\nu} = \frac{8\pi G}{c^4} \text{T}{\mu\nu}$), linking …