COBORDISM AND THE EULER NUMBER
... of N depends only upon M. Moreocer, we may always choose N with Euler number 0 or 1. In dimension 4k - 1, we may choose N with Euler number zero. Proof. Let M = aN, = aN, and let V be the manifold formed by identifying N, and Ni along the boundary. Then the Euler number of V is the sum of the Euler ...
... of N depends only upon M. Moreocer, we may always choose N with Euler number 0 or 1. In dimension 4k - 1, we may choose N with Euler number zero. Proof. Let M = aN, = aN, and let V be the manifold formed by identifying N, and Ni along the boundary. Then the Euler number of V is the sum of the Euler ...
DIETER LÃST (LMU, MPI) - Stony Brook University
... As we have seen, the gravity amplitudes can be expressed as sums over Yang-Mills amplitudes. But we never used the information about the number of colors Nc . • Relation between open and closed string coupling: ...
... As we have seen, the gravity amplitudes can be expressed as sums over Yang-Mills amplitudes. But we never used the information about the number of colors Nc . • Relation between open and closed string coupling: ...
The quantum world is not built up from correlations - Philsci
... this the global state assumption. Perhaps not surprisingly, the assumption holds for classical probability theory and for quantum mechanics on a complex Hilbert space. However, it need not be satisfied in an arbitrary theory, which shows that the theorem is non-trivial. For example, Wootters [9] has ...
... this the global state assumption. Perhaps not surprisingly, the assumption holds for classical probability theory and for quantum mechanics on a complex Hilbert space. However, it need not be satisfied in an arbitrary theory, which shows that the theorem is non-trivial. For example, Wootters [9] has ...
Factorized S-Matrices in Two Dimensions as the Exact
... There are N! disconnected domains in this spacewhere all the particles are far enough from each other and one can neglect interaction between them. Let {x} = {x1 ,..., xN} be the coordinates of the particles and R-the interaction range (we suppose the latter to be finite). Then each domain can be id ...
... There are N! disconnected domains in this spacewhere all the particles are far enough from each other and one can neglect interaction between them. Let {x} = {x1 ,..., xN} be the coordinates of the particles and R-the interaction range (we suppose the latter to be finite). Then each domain can be id ...
Manifestly Covariant Functional Measures for Quantum Field Theory
... inequivalent measure. In particular, we show that if time (and similarly, distances) is discretized into slices spaced a constant physical time apart (i.e., δτ = N δt is constant) that no non-covariant factors appear in the measure. The conclusion that using a different discretizations results in in ...
... inequivalent measure. In particular, we show that if time (and similarly, distances) is discretized into slices spaced a constant physical time apart (i.e., δτ = N δt is constant) that no non-covariant factors appear in the measure. The conclusion that using a different discretizations results in in ...
Can one distinguish quantum trees from the boundary?
... the potential the knowledge of just one spectrum is not sufficient even in the case of a single edge (single interval) [20]. Extending the set of spectral data by including the Titchmarsh-Weyl matrix function (TW-function, see definition below) associated with all boundary vertices, one may reconstr ...
... the potential the knowledge of just one spectrum is not sufficient even in the case of a single edge (single interval) [20]. Extending the set of spectral data by including the Titchmarsh-Weyl matrix function (TW-function, see definition below) associated with all boundary vertices, one may reconstr ...
Mathematical Foundations of Quantum Physics
... Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force. ...
... Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force. ...
Reconstruction of Mature Theory Change: A Theory
... data. For instance, the FTS of classical mechanics consists of the Material Point, the Force and the Inertial System of Reference. The derivative theoretical objects are formed from the basic ones according to certain rules. The sets of derivative objects constitute partial theoretical schemes or P ...
... data. For instance, the FTS of classical mechanics consists of the Material Point, the Force and the Inertial System of Reference. The derivative theoretical objects are formed from the basic ones according to certain rules. The sets of derivative objects constitute partial theoretical schemes or P ...
Time reversal in classical electromagnetism - Philsci
... world is no longer allowed. This seems odd: it’s the same world after all, just described using one set of coordinates rather than another. How could the one be allowed by our theory and the other not? Indeed, this does not make much sense unless one supposes that the theory, as stated in coordinate ...
... world is no longer allowed. This seems odd: it’s the same world after all, just described using one set of coordinates rather than another. How could the one be allowed by our theory and the other not? Indeed, this does not make much sense unless one supposes that the theory, as stated in coordinate ...
Fractals as macroscopic manifestation of squeezed
... (phase locking) the whole set of modes a condensed in the state |αi. We have thus a correlation mediated by a phase (not by a force). Since coherent states are defined only in the limit n → ∞, the summation in Eq. (18) cannot be approximated by any finite number of terms and we thus see that coheren ...
... (phase locking) the whole set of modes a condensed in the state |αi. We have thus a correlation mediated by a phase (not by a force). Since coherent states are defined only in the limit n → ∞, the summation in Eq. (18) cannot be approximated by any finite number of terms and we thus see that coheren ...
An Introduction to the Mathematical Aspects of Quantum Mechanics:
... 1. (φ, aψ + bν) = a(φ, ψ) + b(φ, ν); 2. (ψ, φ) = (ψ, φ)∗ , where the asterisk denotes complex conjugation. 3. kψk2 = (ψ, ψ) > 0 unless ψ = 0 Note 1.b. Note that statement c of Lemma 1.2.1 is not quite correct. To be precise, we should say that if kψk2 = 0 then ψ(x) = 0 almost everywhere, i.e. ...
... 1. (φ, aψ + bν) = a(φ, ψ) + b(φ, ν); 2. (ψ, φ) = (ψ, φ)∗ , where the asterisk denotes complex conjugation. 3. kψk2 = (ψ, ψ) > 0 unless ψ = 0 Note 1.b. Note that statement c of Lemma 1.2.1 is not quite correct. To be precise, we should say that if kψk2 = 0 then ψ(x) = 0 almost everywhere, i.e. ...
Fractionalization in an easy-axis Kagome antiferromagnet
... approximately J z to states with any nonzero S ˝ . Hence the ground state has in this sense a ‘‘spin gap.’’ Thus the easyaxis generalized Kagome antiferromagnet has no XY spin order, but translational symmetry breaking is not precluded. More subtle aspects of this model are less evident. In particul ...
... approximately J z to states with any nonzero S ˝ . Hence the ground state has in this sense a ‘‘spin gap.’’ Thus the easyaxis generalized Kagome antiferromagnet has no XY spin order, but translational symmetry breaking is not precluded. More subtle aspects of this model are less evident. In particul ...
as a PDF
... Furthermore, the main quantum numbers for fermions are charge and spin, but these are common throughout any one generation, e.g. e, μ, τ. Parity, a spatial inversion (mirroring) of physical properties, is another way to differentiate the species, (hence ‘mirror matter’, as Robert Forward termed it). ...
... Furthermore, the main quantum numbers for fermions are charge and spin, but these are common throughout any one generation, e.g. e, μ, τ. Parity, a spatial inversion (mirroring) of physical properties, is another way to differentiate the species, (hence ‘mirror matter’, as Robert Forward termed it). ...