Doubt regarding explanation of dominance of classical paths at 34:35. I think it is to do with the fact that the paths 'near' the classical path vary insignificantly (order epsilon^2) and so the phases there will add up whereas they will cancel since the action varies tremendously everywhere else. This effect will grow more and more prominent as hbar tends to zero. I don't think it has anything to do with the value of the phase being 1 as you pointed out. Please clarify if my thinking has a conceptual problem. Thank you!
what do you exactly mean by the expression δq(t1)/ δq(t2) = δ(t1-t2) (at time 24:37) ? I understand the δq(t) is a function of t, and by definition of a function, it can have different values at different times. what is so special about this? and how does dividing δq at two different times give a Dirac Delta function? If t1=t2, wouldn't the ratio just be 1? and wouldn't it be some arbitrary non-zero number when they are not equal? I don't understand that equation at all.
If time were discrete, your argument would go through and we would get the Kronecker delta. However, time is continuous and hence the appearance of the Dirac delta function is more natural. We are defining what is called the "functional derivative".
Hi. I actually had a question around the timestamp 7:40 where you define the total time derivative for the Lagrangian. From what I have understood in my previous courses on classical mechanics, the total time derivative can be defined in this way WHEN the Lagrangian is evaluated on the trajectory. What I mean to say is, until you talk about a particular trajectory Q(t), the Lagrangian is just some function that takes in 2N Real numbers and spits out a Real number. That's all. Unless you particularly talk about a given trajectory, there are no "implicit" time dependencies. It's when you say that "we evaluate the Lagrangian on some trajectory Q(t)" does the point that coordinates and velocities have implicit time-dependence makes sense i.e. we substitute q=Q(t) and q_dot= dQ(t)/dt into the Lagrangian. So how does that definition of the total time derivative make sense until you actually define particle trajectories?
You can in that point still think of Lagrangian as a function of 2N or 2N+1 parameters in case of explicit time dependence, the full derivative by some variable in that specific example makes sense, it is just the derivative by a variable and in the case of one independency just evaluates to zero. However, it is much more interesting and practical to think of trajectories. The Lagrangian is no use without that concept.
you should give topic names in the link with videos , so that it is easier to access the topic you want to revise/understand.... merely giving the module name and lecture name does not help(anyone) at all!!
Imagine! The idea of planning a course that's going out on the Internet! Don't you think that's a bit radical? Pedagogogogerry is an ancient art. Thousands of years of students have looked at the back of teachers' heads as they wrote on blackboards. Now we can use the miracle of electronics to bring the backs of teachers' heads to the masses. And you want to upset that by planning something different? Oh, the horror!
Writing only mathematics without discussing the physical significance is of no use. Make the contests to life driving students' imagination in class and later let them develop the mathematics based on the understanding of theory. Physics is interesting to learn.
This is an advanced elective course aimed at senior undergraduates and final year students in the two-year Masters course in Physics. I believe that Mathematics is the language in which Physical Sciences are spoken contrary to what you might gather from reading popular science books. I worked hard to teach all the mathematics that was needed in my course. Of course, if you ever give a lecture series on this topic without mathematics, do send me an email. I am always ready to learn new methods of teaching.
@@SureshGovindarajan u explained it very well prof..Math is only language in which technical details can be encoded than speaking sentences.. I think u are more inspired from yr colleague Dr. V. Balakrishnan
@@karabomothupi9759 How did u and this so called "great professor" judge him that he's a non scientific person. He clearly said that what's the use of writing equations in the black board without explaining Physical significance. And my friend, please watch other lectures and speak before you know things. And also one things, since u said about Niel deGrasse Tyson, why would someone choose classical field theory and speak about Physical significance and complain about lack of explanation of physical significance.?.…...This field is not even popular science.
@@SureshGovindarajan sir you explained every word of this course we are happy with it ,however some people don't understand that ,the calculus of variation is a part of mathematical physics and what is explained in this video is itself the physical significance of the calculus of variation .people should clear their basic concepts of mathematics before coming to this course of field theory .I'm a student of guahati University from assam in bsc 5th sem and I learnt tensors and other things before coming to this course .
Thank you NPTEL and @SureshGovindarajan for such a brilliant course
His writing, speech and thinking are so clear, this is a joy to listen to!
Doubt regarding explanation of dominance of classical paths at 34:35. I think it is to do with the fact that the paths 'near' the classical path vary insignificantly (order epsilon^2) and so the phases there will add up whereas they will cancel since the action varies tremendously everywhere else. This effect will grow more and more prominent as hbar tends to zero. I don't think it has anything to do with the value of the phase being 1 as you pointed out. Please clarify if my thinking has a conceptual problem. Thank you!
what do you exactly mean by the expression δq(t1)/ δq(t2) = δ(t1-t2) (at time 24:37) ? I understand the δq(t) is a function of t, and by definition of a function, it can have different values at different times. what is so special about this? and how does dividing δq at two different times give a Dirac Delta function? If t1=t2, wouldn't the ratio just be 1? and wouldn't it be some arbitrary non-zero number when they are not equal? I don't understand that equation at all.
If time were discrete, your argument would go through and we would get the Kronecker delta. However, time is continuous and hence the appearance of the Dirac delta function is more natural. We are defining what is called the "functional derivative".
@SureshGovindarajan can you please tell me which textbook should I follow along with this lecture series?
Hi. I actually had a question around the timestamp 7:40 where you define the total time derivative for the Lagrangian. From what I have understood in my previous courses on classical mechanics, the total time derivative can be defined in this way WHEN the Lagrangian is evaluated on the trajectory. What I mean to say is, until you talk about a particular trajectory Q(t), the Lagrangian is just some function that takes in 2N Real numbers and spits out a Real number. That's all. Unless you particularly talk about a given trajectory, there are no "implicit" time dependencies. It's when you say that "we evaluate the Lagrangian on some trajectory Q(t)" does the point that coordinates and velocities have implicit time-dependence makes sense i.e. we substitute q=Q(t) and q_dot= dQ(t)/dt into the Lagrangian.
So how does that definition of the total time derivative make sense until you actually define particle trajectories?
You can in that point still think of Lagrangian as a function of 2N or 2N+1 parameters in case of explicit time dependence, the full derivative by some variable in that specific example makes sense, it is just the derivative by a variable and in the case of one independency just evaluates to zero. However, it is much more interesting and practical to think of trajectories. The Lagrangian is no use without that concept.
So you don't undestend well. Total derivative of a function it's math, not physics
Anyone have the book of AK roychaudhary. Classical mechanics. I really need it
Thank you sir for providing this wonderful lecture series ,I learnt a lot from this course
you should give topic names in the link with videos , so that it is easier to access the topic you want to revise/understand.... merely giving the module name and lecture name does not help(anyone) at all!!
Imagine! The idea of planning a course that's going out on the Internet!
Don't you think that's a bit radical? Pedagogogogerry is an ancient art. Thousands of years of students have looked at the back of teachers' heads as they wrote on blackboards. Now we can use the miracle of electronics to bring the backs of teachers' heads to the masses.
And you want to upset that by planning something different? Oh, the horror!
I am really sorry about this. However, I maintain a page for this course which does this. sgovindarajan.wikidot.com/cftontheweb
@@SureshGovindarajan Thanks so much for posting the course page, and for teaching this fantastic class Sir :). Kindest regards from Canada
@@JaGWiREE Thank you.
What are the mathematical pre requisites for this course
Nevermind! It's out there in the webpage that professor maintains! By the way the webpage is pretty good! Well structured!
@@nsumanth18 what is the webpage? Can't find it
Excellent lectures!
Great Work !
thk u Sir... and NPTEL.
Writing only mathematics without discussing the physical significance is of no use. Make the contests to life driving students' imagination in class and later let them develop the mathematics based on the understanding of theory. Physics is interesting to learn.
This is an advanced elective course aimed at senior undergraduates and final year students in the two-year Masters course in Physics. I believe that Mathematics is the language in which Physical Sciences are spoken contrary to what you might gather from reading popular science books. I worked hard to teach all the mathematics that was needed in my course. Of course, if you ever give a lecture series on this topic without mathematics, do send me an email. I am always ready to learn new methods of teaching.
@@SureshGovindarajan u explained it very well prof..Math is only language in which technical details can be encoded than speaking sentences.. I think u are more inspired from yr colleague Dr. V. Balakrishnan
You are looking for Neil Degrassi Tyson. This is serious physics my guy. Go elsewhere
@@karabomothupi9759 How did u and this so called "great professor" judge him that he's a non scientific person. He clearly said that what's the use of writing equations in the black board without explaining Physical significance. And my friend, please watch other lectures and speak before you know things. And also one things, since u said about Niel deGrasse Tyson, why would someone choose classical field theory and speak about Physical significance and complain about lack of explanation of physical significance.?.…...This field is not even popular science.
@@SureshGovindarajan sir you explained every word of this course we are happy with it ,however some people don't understand that ,the calculus of variation is a part of mathematical physics and what is explained in this video is itself the physical significance of the calculus of variation .people should clear their basic concepts of mathematics before coming to this course of field theory .I'm a student of guahati University from assam in bsc 5th sem and I learnt tensors and other things before coming to this course .