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Quantum gravity Quantum gravity is the study of unification of quantum theory and general relativity starting from quantum theory. The methods considered possible in the past were: 1) starting with general relativity, develop a quantum version; 2) start with quantum theory and form a relativistic version similar to Dirac’s equation in special relativity; 3) develop a totally new mathematics like string or M theory. Evan’s equations show that quantum theory can be developed from general relativity. Quantum mechanics A physical theory that describes the behavior of matter at very small scales. The quantum theory attempts to explain phenomena that classical mechanics and electrodynamics were unable to explain. It has provided highly accurate descriptions of various processes. Quantum number A label on a quantum state. It can give the number of quanta of a particular type that the state contains. If the electric charge on a particle were given as an integer multiple of the electron's charge then that would be a quantum number. Quarks Mathematically quarks make sense, but physically they are unlikely to exist as discrete particles. The implication is that they are curvature or energy states. Quarks have fractional charge, but are supposed to be fundamental. By definition a fundamental charge cannot be divided. It then seems that quarks are either divisible and not fundamental or they are not there at all. Rather they are representations of curvature states. They were found by bouncing energy off nuclei and curve fitting the scattering patterns. They cannot exist outside a triplet. Most likely they are a substructure that is pure curvature and torsion rather than any discrete particle like object. The three curvatures may reflect existence in three dimensions. R The Ricci scalar - a measure of curvature. Curvature in four dimensions is described by the Riemann curvature tensor. Two dimensional curvature can be described by the Ricci scalar. In the limit of special relativity, κ 2 = R where κ (or κ in some texts) is 1/r of an osculating circle drawn at a point or dot. See curvature. The Evans equations indicate that curvature and wave number are related; a new understanding. Rank Number of indices. A zero rank tensor is a scalar – a simple number. A 4-vector is a rank one tensor. A four dimensional tensor is a rank two tensor. 342
Reference Frame A reference frame is a system, particle, spaceship, planet, a region in spacetime say near a black hole, etc. The reference frame has identical gravity and velocity throughout its defined region. Everything in it has the same energy density. Sometimes it is necessary to shrink the size of the reference frame to a size near a point. If small enough of a region, then the laws of special relativity (Lorentz) apply. This is what is meant by all points are Lorentzian. Renormalization The sum of the probability of all calculated quantum outcomes must be positive one – 100%. We cannot have a negative chance or 120% or 80% chance of an occurrence. Quantum mechanics had problems with infinite quantities resulting in some calculations where volume of a particle was assumed to be zero. To avoid these mathematical renormalization techniques were developed in quantum electrodynamics. A finite volume is assumed without proof. Imagine a volume going to zero while the amount of mass is constant. The density goes to infinity if the volume goes to zero which is obviously wrong in reality although it is correct mathematically. The calculation: ρ = m/V (density = mass / volume). When V = 0, then ρ = m / V = ∞. By assuming that V cannot get smaller than say, h 3 , the density will approach a very high value, but not infinity; the equation then produces a reasonable result. Evans has found that mV = k(h/2πc) 2 . V defined here is limited. Renormalization by assuming some arbitrary small but positive volume is no longer necessary. The causal Evans volume can be used instead.. Ricci tensor Rµν is the Ricci tensor. It is the trace of the Riemann curvature tensor. It is a mathematical object that controls the growth rate of volumes in a manifold. It is a part of the Einstein tensor and is used to find the scalar curvature. It can be thought of as the sum of the various curvatures spanned by a tetrad’s orthonormal vector and the corresponding vector in the base manifold. Any spacetime manifold can have a negative curvature, but a positive Ricci curvature is more meaningful. Riemann geometry Non-Euclidean geometry of curved spaces. Einstein gravitation is described in terms of Riemann geometry. Spacetime curvature refers to Riemannian spacetime curvature, Rλµνκ; there are other types of curvature. If any of the elements of Rλµνκ are not zero then Riemannian spacetime curvature is not zero. 343
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1 The Evans Equations of Unified Fi
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3 Torsion .........................
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5 Standard Model with Higgs versus
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Do keep in mind Einstein’s statem
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postulate of general relativity. In
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thought were incorrect. Einstein wa
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8 Figure I-1 Spacetime Newton’s f
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In order to do calculations in the
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12 Figure I-4 The Four Forces Gravi
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The Particles There are stable, lon
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Chapter 1 Special Relativity 16 The
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unnoticeable, for low velocities, b
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The nature of spacetime is the caus
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Figure 1-3 Graph of Stress Energy i
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An example is shown in Figure 1-4.
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There are many short form abbreviat
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The cross product is not defined In
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form. Given that they are discrete
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curvature, but does not allow spinn
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Chapter 2 General Relativity Introd
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However, acceleration and a gravita
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Energy density reference frames T =
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infinity - at distances where the c
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42 Figure 2-4 Visualizing Curved Sp
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Curvature Curvature is central to t
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We showed that gravitation is curva
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Figure 2-9 Base Manifold with Eucli
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In Figure 2-10 at the top is the te
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We put the object in the tangent sp
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The metric tensor is important in g
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Chapter 3 Quantum Theory Quantum Th
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1930’s when it became well establ
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that we have such accuracy as we ha
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spaces. The formulation is beyond t
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frame where measurement is made.) P
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Quantum Numbers The equations below
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Quantum Gravity and other theories
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x time, or momentum x distance, or
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72 E = pc and E = ħ ω and therefo
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When the Planck units are used, it
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76 ms is spin quantum number. It is
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experiments and to describe events.
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are the same space; this is a mathe
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82 If a curve is described by y = a
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Scalar, or Inner Product The dot pr
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Figure 4-5 Cross Product a 86 The v
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product produces surfaces that cut
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4-Vectors and the Scalar Product An
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definite - it is a real distance. I
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Einstein is the tensor defined as G
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With some operations one must add t
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Alternately, a set of basis matrice
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Figure 4-12 100 0 2 1 3 q can repre
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Contravariant and covariant vectors
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The scalars, whether real or imagin
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106 2 _ 1 ∂ 2 c 2 ∂ t 2 can be
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Covariant Exterior Derivative D ∧
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Chapter 5 Well Known Equations Intr
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V = IR. A circuit is a completed ci
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The standard definition of magnetic
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Another way of stating this is that
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Figure 5-4 Ampere's and Faraday’s
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Newton’s law of gravitation 120 A
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Figure 5-6 Fields Poisson’s Equat
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This is a differential operator use
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The Evans equations indicate that R
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Compton and de Broglie wavelengths
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Here ħ = h / 2π = Planck’s cons
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Mathematics and Physics To a certai
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Chapter 6 The Evans Field Equation
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Then the wave equation was develope
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138 q ab µν = q a µq b ν q ab
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From the basic structure of equatio
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142 Rµν - ½ Rgµν = kTµν Eins
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original vector - its orientation i
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The electromagnetic and weak fields
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In more mechanical terms, energy an
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Figure 6-8 Abstract Fiber Bundle an
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The other three fields - electromag
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Figure 6-9 The spin connection and
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Evans Field Equation Extensions R =
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The real physical solutions the wav
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160 Another way to look at the equa
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determined by geometry. This makes
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index, it is generally covariant -
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It is also possible to represent bo
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Electromagnetism 168 The B (3) fiel
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Strong force If tetrad index “a
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neutron into other more stable curv
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explanation for the Aharonov-Bohm a
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ORIGIN Einstein / Hilbert (1915) Ev
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then we found it and used it to des
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Very Strong Equivalence Principle T
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Figure 8-2 Separation of Forces PRI
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Note that physics texts often say t
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criteria for dark matter. We know t
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Figure 8-5 Spinning Spacetime The s
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this gives the influence of gravita
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In all the forms of the tetrad, the
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Spacetime curvature in and around p
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The Evans Wave Equation Figure 8-8
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λ is the wavelength. It can be app
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λde B = ħ / p = ħ / mv (6) where
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where ψ a µ is a tetrad. Therefor
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The components of R = -kT originati
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Relationship between r and λ Profe
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Figure 9-4 Curvature and Wavelength
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One may tentatively assume that the
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The first gives us the Principle of
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Chapter 10 Replacement of the Heise
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p b µ = ћ κ b µ (2) The positio
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The volumes here are derived from V
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The Heisenberg uncertainty principl
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Chapter 11 The Evans B (3) Spin Fie
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where g = e/ћ for one photon; e is
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Figure 11-3 shows the circle turnin
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the curvature very slight at the ea
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The magnetic field components are r
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The B (3) field is the fundamental
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The present standard model uses con
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Using Einstein’s index contracted
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unnecessary and it has been shown t
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Figure 12-4 Momentum Exchange p 3 p
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Figure 12-6 Equations in the Tangen
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were still unknown. However it is o
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Consider an experiment where a beam
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Here κ is wave number, ds is the i
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the Evans unified field theory. Sim
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Figure 13-6 Ordinary Stokes is a ci
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Chapter 14 Geometric Concepts Intro
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where φ is the gravitational poten
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Just what equation will be found to
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where e is the charge of the electr
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have quantization of general relati
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The scalar curvature, R, is defined
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Chapter 15 A Unified Viewpoint Intr
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Asymmetry is a combination of symme
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We know energy density increase is
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G q a µ = kT q a µ. Is one formul
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unknowable measurements. ħ is the
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and their respective ratios was,
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It seems inevitable that we will fi
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Quantum mechanics presented us with
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Evans’ equations the electromagne
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A naïve description would be that
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Note that we are still missing some
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Oscillatory Universe The equation m
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We do not have a definite mechanica
Page 298 and 299: Glossary There are some terms here
Page 300 and 301: AIAS Alpha Institute for Advanced S
Page 302 and 303: The B (3) field and O(3) electrodyn
Page 304 and 305: The calculations to get coordinates
Page 306 and 307: Connections Circular Basis The equa
Page 308 and 309: Elie Cartan worked out an approach
Page 310 and 311: A covariant component is a physical
Page 312 and 313: Covariant derivative operator (∇
Page 314 and 315: Curvature at a given point P has a
Page 316 and 317: Dimension While mathematically well
Page 318 and 319: Einstein Field Equation The equatio
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Page 322 and 323: Fields explain “action at a dista
Page 324 and 325: Fundamental Particle A particle wit
Page 326 and 327: Geometric units Conversion of mass
Page 328 and 329: describes electrodynamics. It is no
Page 330 and 331: Index Typically Greek letters are u
Page 332 and 333: Isomorphism A 1:1 correspondence. J
Page 334 and 335: Local A very small region of spacet
Page 336 and 337: Another use is with the Dirac and o
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Page 340 and 341: Time invariance (or symmetry under
Page 342 and 343: Dual vectors = one forms = covector
Page 344 and 345: Meson - Any of a family of subatomi
Page 346 and 347: The Evans phase law is: This is app
Page 350 and 351: Riemann tensor Riemann calculates t
Page 352 and 353: Schrodinger's Equation ∇ 2 Ψn =
Page 354 and 355: The spin connection may be best des
Page 356 and 357: α angular acceleration; fine struc
Page 358 and 359: Rotation and reflection of a triang
Page 360 and 361: Next is O(3) electrodynamics which
Page 362 and 363: Rank is indicated by the number of
Page 364 and 365: A spin structure is locally a tetra
Page 366 and 367: q a µ can be defined in terms of a
Page 368 and 369: The torsion of a curve is a measure
Page 370 and 371: our real four dimensional spacetime
Page 372 and 373: Wave or Quantum Mechanics Study of
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