Around 50:00, Dr Dijkgraaf mentions that it's a good exercise to compute the partition function on the 2-torus. Has anybody tried computing this? I've tried to calculate it myself, but I think my answer is slightly off track, and I can't seem to find that particular calculation done anywhere else to verify with.
The answer is on the screen. If you are just interested in the case genus = 1, it is even easier: the cylinder S^1 x [0,1] corresponds to the identity on the Hilbert space H. Gluing the two ends together gives the trace of this operator. So \Phi_{S^1 x S^1} = dim(H).
I was a complete outsider and this was a really fun intro to the theory. Thanks a lot! Does anyone know why a TQFT on M x [0,t] would mean wave function evolution over time t but this depends on the metric? TQFT is supposed to ignore the metric.
In the a functorial picture for quantum field theory, Mx[0,t] should be mapped to the time evolution operator on spatial slice M for time t. In QM this would be e^{-iHt/h}. In a TQFT there are no dynamics at all. The Hamiltonian is zero. So indeed M x [0,t] will be mapped to the identity as expected from the definition of a TQFT.
No question = audiences can get confused easily and their concerns may not be resolved, making the later stuff even more confusing. Also due to the question-discouraging nature of academic talks, the actual proportion of questions is sometimes much lower than the amount of confusion in the audiences.
DdDark energy exsist as a FIELD INVARIANCE of Space configuration "PHASALITY" using a form of Spatial automorphism to auto regulate (gauge) ( ENGAGE) or Break Symmetry , the amount of energy , time , Velocity ( NEWTONIAN MECHANICS) plus {frequency) , and Volume required to Continuous Transform Any particle matter of that SPACE TIME "Configuration" ( FIELD, TENSOR, PARTICLE WAVE ENERGY PAIRING ) (LANGRAININ MECHANIC ) at that specific location ,` or at any future location in that Space Time, Ex. photons or light like particles Traveling in a straight line at a Fraction of speed of light (ECLUDIEAN SPACETIME DILATION) gives rise to Baryonic mass and (RADIOACTIVE DECAY ) through Quasi-Local Fields INTERACTION SCALAR FIELD "PHASING" like (HIGGS BOSON) particles fields , Extending into like matter electron proton ect. thru When ( Riemann space) gravity, electromagnetic, nuclear Strong force is engaged thru Baryionic Field Boson interaction the electromagnetic Photon Particle enters and engages Curvatured Space. Reaching infinite mass (NEAR INFINITE PHASALITY) for that particle wave location causing a curved Deceleration we call gravity.and Electromagnetism Entanglement happens by Shears TRANSFORMATION of this Baryonic mass/particle/ when Space itself shears and Rotates , Like a Automorphism mapping of Space, So all FIELD in that Space becomes INVARIANT Orients itself, to a common point enabling one PARTICLES (like the MUON) to exist as a COLLAPSING Wave Function in Two Different Non-Local SPACES or fields. (PHASE) or thru a local Field SYMMETRY ,and Because Information travels in a Linear fashion in 3 Dimension Space , We olny become Aware of this Spacetime Information by attempting to Communicate outside our everyday 4 Dimensional Spacetime . and Not Seeing ,or Receiving anything back then we say mass is missing, Entangled particles don't need this Same Time information to Communicate because it Exists at every point in the Entangled PARTICLES BARYONIC MASS WAVE function . The SpaceTime Coordinates has Shared Merging at a Every Point in the field .So Field Entaganelment is (BOTH)a Attractive Force Within a mutual , Baryonic LEPTON MUON MESON Field space is a Repulsive Force where the Wave Particle are Running Away from Itself as a non local non mutual (RELATIVISTIC )field, So when you observe or try to measure the Particle the Wave function does not Collapses because the wave and Particle exsist as non mutual independent Quasi local Field OVER A DISTANCE WAVE or a Gauge less field for Relativistic and Quantum Field Entanglement the Field Symmetry Collapse of breaks from a ( DIALATED SCALAR Field So Dark Matter Could be a Non-Localized Spacetime like a Black Hole with Equally distributed gravitational mass and inertial mass .Analysis of high velocity Nuetrino burst from Gamma rays as Observed from our 4 Dimensional Spacetime Frame of Reference might confirm this. Were the Nuetrino ACT as a SYMMETRY break of ENTROPY (Gauge Field) breaks and lose its Orientation.and this ROTATIONAL SYMMETRY break can be Non-Local or Quasi-Local Field when all Particle waves FIELD and SPACES becomes INVARIANT UNDER A mutual FLAT MANIFOLD
Around 50:00, Dr Dijkgraaf mentions that it's a good exercise to compute the partition function on the 2-torus. Has anybody tried computing this? I've tried to calculate it myself, but I think my answer is slightly off track, and I can't seem to find that particular calculation done anywhere else to verify with.
Recall that's equivalent to computing it on a plane with periodic boundary conditions
The answer is on the screen. If you are just interested in the case genus = 1, it is even easier: the cylinder S^1 x [0,1] corresponds to the identity on the Hilbert space H. Gluing the two ends together gives the trace of this operator. So
\Phi_{S^1 x S^1} = dim(H).
I was a complete outsider and this was a really fun intro to the theory. Thanks a lot!
Does anyone know why a TQFT on M x [0,t] would mean wave function evolution over time t but this depends on the metric? TQFT is supposed to ignore the metric.
In the a functorial picture for quantum field theory, Mx[0,t] should be mapped to the time evolution operator on spatial slice M for time t. In QM this would be e^{-iHt/h}.
In a TQFT there are no dynamics at all. The Hamiltonian is zero. So indeed M x [0,t] will be mapped to the identity as expected from the definition of a TQFT.
hi there are notes about this?
Questions are a pain. Ask him after the lecture!
you clearly don't understand how physics is done
No question = audiences can get confused easily and their concerns may not be resolved, making the later stuff even more confusing.
Also due to the question-discouraging nature of academic talks, the actual proportion of questions is sometimes much lower than the amount of confusion in the audiences.
Questions are indispensable. If you don't even understand this, don't even bother watching this lecture.
@@badmintongo4832 😂🤣
DdDark energy exsist as a FIELD INVARIANCE of Space configuration "PHASALITY" using a form of Spatial automorphism to auto regulate (gauge) ( ENGAGE) or Break Symmetry , the amount of energy , time , Velocity ( NEWTONIAN MECHANICS) plus {frequency) , and Volume required to Continuous Transform Any particle matter of that SPACE TIME "Configuration" ( FIELD, TENSOR, PARTICLE WAVE ENERGY PAIRING ) (LANGRAININ MECHANIC ) at that specific location ,` or at any future location in that Space Time, Ex. photons or light like particles Traveling in a straight line at a Fraction of speed of light (ECLUDIEAN SPACETIME DILATION) gives rise to Baryonic mass and (RADIOACTIVE DECAY ) through Quasi-Local Fields INTERACTION SCALAR FIELD "PHASING" like (HIGGS BOSON) particles fields , Extending into like matter electron proton ect. thru When ( Riemann space) gravity, electromagnetic, nuclear Strong force is engaged thru Baryionic Field Boson interaction the electromagnetic Photon Particle enters and engages Curvatured Space. Reaching infinite mass (NEAR INFINITE PHASALITY) for that particle wave location causing a curved Deceleration we call gravity.and Electromagnetism
Entanglement happens by Shears TRANSFORMATION of this Baryonic mass/particle/ when Space itself shears and Rotates , Like a Automorphism mapping of Space, So all FIELD in that Space becomes INVARIANT Orients itself, to a common point enabling one PARTICLES (like the MUON) to exist as a COLLAPSING Wave Function in Two Different Non-Local SPACES or fields. (PHASE) or thru a local Field SYMMETRY ,and Because Information travels in a Linear fashion in 3 Dimension Space , We olny become Aware of this Spacetime Information by attempting to Communicate outside our everyday 4 Dimensional Spacetime . and Not Seeing ,or Receiving anything back then we say mass is missing,
Entangled particles don't need this Same Time information to Communicate
because it Exists at every point in the Entangled PARTICLES BARYONIC MASS WAVE function . The SpaceTime Coordinates has Shared Merging at a Every Point in the field .So Field Entaganelment is (BOTH)a Attractive Force Within a mutual , Baryonic LEPTON MUON MESON Field space is a Repulsive Force where the Wave Particle are Running Away from Itself as a non local non mutual (RELATIVISTIC )field, So when you observe or try to measure the Particle the Wave function does not Collapses because the wave and Particle exsist as non mutual independent Quasi local Field OVER A DISTANCE WAVE or a Gauge less field for Relativistic and Quantum Field Entanglement the Field Symmetry Collapse of breaks from a ( DIALATED SCALAR Field
So Dark Matter Could be a Non-Localized Spacetime like a Black Hole with Equally distributed gravitational mass and inertial mass .Analysis of high velocity Nuetrino burst from Gamma rays as Observed from our 4 Dimensional Spacetime Frame of Reference might confirm this. Were the Nuetrino ACT as a SYMMETRY break of ENTROPY (Gauge Field) breaks and lose its Orientation.and this ROTATIONAL SYMMETRY break can be Non-Local or Quasi-Local Field when all Particle waves FIELD and SPACES becomes INVARIANT UNDER A mutual FLAT MANIFOLD
what are you saying dude
wow, you almost put these words in an order that makes sense